Question

In Exercises 1–2,

find a. v. u,| v|,|u|

b. the cosine of the angle between v and u

c. the scalar component of u in the direction of v

d. the vector proj vu.

1. v = 2i - 4j + 25k, u =-2i + 4j - 25k

2. v = (3/5)i + (4/5)k, u = 5i+12j

Expert Solution

Want to see the full answer?

Check out a sample Q&A here
Blurred answer
Students who’ve seen this question also like:
Linear Algebra: A Modern Introduction
Linear Algebra: A Modern Introduction
4th Edition
ISBN: 9781285463247
Author: David Poole
Publisher: Cengage Learning
Not helpful? See similar books
marketing sidebar icon
Want to see this answer and more?
Experts are waiting 24/7 to provide step-by-step solutions in as fast as 30 minutes!*
*Response times may vary by subject and question complexity. Median response time is 34 minutes for paid subscribers and may be longer for promotional offers.

Related Calculus Q&A

Find answers to questions asked by students like you.

Q: In Exercises 1–2, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar…

A: given

Q: In Exercises 1–3, find a. v. u,| v|,|u| b. the cosine of the angle between v and u c. the scalar…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: In Exercises 1-8, find a. v.u, v], |u| b. the cosine of the angle between v and u c. the scalar…

A: Click to see the answer

Q: In Exercises 1-8, find a. v•u, v]. Ju| b. the cosine of the angle between v and u c. the scalar…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: In Exercises 15–18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: We'll answer the first question since the exact one wasn't specified . Please submit a new question…

Q: In Exercises 9–14, sketch the coordinate axes and then include the vectors u, v, and u * v as…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: Triangles in Space

A: Area of triangle formed by P,Q,R is given by  Area=PQ ⇀×PR⇀2 UNIT VECTOR is given by  unit vector=PQ…

Q: Dot Product and Projections in Exercises 1–8, find

A: 1. Given v=2i-4j+5k, u=-2i+4j-5k (a) To find v·u. v·u=2i-4j+5k·-2i+4j-5k=2·-2+-4·4+5·-5=-4-16-5=-25…

Q: In Exercises 1-8, find a. v•u, |v], |u| b. the cosine of the angle between v and u c. the scalar…

A: Click to see the answer

Q: Find the angles between the vectors in Exercises 9–12 to the nearest hundredth of a radian. 9. u =…

A: Hey, since there are multiple questions posted, we will answer first question. If you want any…

Q: Find the angle between the planes whose vector equations are F-(2i +2j–3k) =s. Sand 7(3) –3} +Sk) =…

A: The equation of the given planes are r→·2i^+2j^-3k^=5 and r→·3i^-3j^+5k^=3. It is known that if n→1…

Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: Click to see the answer

Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Find the magnitude of the vector U = 9i + 12j. |U : %3D

A: If the vector is given:   w=ai+bj+ck   Then its magnitude will be:   w=a2+b2+c2

Q: In Exercise 24, find the angle θ between the vectors (a) in radians and (b) in degrees. 24. u = ⟨1,…

A: Given: u = ⟨1, 0, −3⟩, v = ⟨2, −2, 1⟩

Q: compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors. What do you…

A: Given: Compute the dot products i ⋅ j, i ⋅ k, and j ⋅ k for the unit coordinate vectors.

Q: O let A = i+2j-K, B=-i+j+K, Esi+k, 5z i+2j-K which vectors are: @ perpen dicular Parallel

A: Our are objectives to check which vectors are parallel and which vectors are perpendicular

Q: Let u =j- 3k, v = - 9i + 3j – 3k, w = 3i -j+ k. Which vectors, if any are (a) perpendicular? (b)…

A: Click to see the answer

Q: Given the vector u (- 6, 2), find the magnitude and angle in which the vector points (measured…

A: Click to see the answer

Q: In Exercises 15-18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: Answer

Q: For Exercises 19–28, use vectors u = (-4, 1) ,v = (5, -2) , and w = (0,6) to perform the indicated…

A: Given vectors are

Q: For Exercises 19–28, use vectors u = (-4, 1) ,v = (5, -2) , and w = (0,6) to perform the indicated…

A: Click to see the answer

Q: For Exercises 19–28, use vectors u = (-4, 1) ,v = (5, -2) , and w = (0,6) to perform the indicated…

A: Click to see the answer

Q: Explain why u + v • w _is not defined, where u, v, and w are nonzero vectors.

A: Given 3 non zero vectors : u , v and w. We need to explain why  u + v . w is not defined.

Q: Explain why u + v ∙ w is not defined, where u, v, and w are nonzero vectors.

A: Let us assume that u,v, and w are nonzero vectors.  The dot product of the vector of the scalar…

Q: Find the component of the force 5i+7j-k in the direction of the displacement PQ, where P(3,0,1) and…

A: The given force is

Q: Find the angle e between the vectors. u = (0, 0, 1, 0), v = (3, 3, 3, 3) radians

A: Click to see the answer

Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: Find a) The cosine of the angle between vand u b) The vector proj} 1) v=10i+11j-2k , u=2i+2j+k 101 1…

A: Click to see the answer

Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

A: Click to see the answer

Q: Find the unit vector having the same direction as v. v = 3i + - 4j O A. u= 15i + - 20j OB. u- - 5 B.…

A: Click to see the answer

Q: Find the angle between the vectors ā and b where ā = i + 2j – k and b = -i+j- 2k. %3D

A: The angle between the two vectors  a→=axi^+ayj^+azk^b→=bxi^+byj^+bzk^ can be calculated as cos…

Q: Q1: - Calculate the angle between two vectors M=2 ax+4 ay and N= 6 ay - 4 az using %3D a) The cross…

A: Click to see the answer

Q: In Exercises 17 and 18, find |v| , |u| , v .u, u. v, v * u, u * v, |v * u| , the angle between v and…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

Q: Given the vector →u=⟨−3,−1⟩, find the magnitude and angle in which the vector points (measured…

A: Click to see the answer

Q: Let u=j-5k, v=5i-j+k, w=-10i+2j-2k Which vectors, if any, are perpendicular? Which are parallel

A: Click to see the answer

Q: Find the angles between the vectors in Exercises 9–12 to the nearest hundredth of a radian. 9. u =…

A: Click to see the answer

Q: 15. Given the vector u (2i + 5j) and vector v = (3i + 4j), find the dot product u v %3D

A: We have to find the dot product of given vectors.

Q: One of the components of cross ultiplication of the vectors A = 21 + 3 *:j + 4k and B = i-2j+3k is…

A: Given vectors are A=2i+3j+4k and B=i-2j+3k. Cross multiplication of given vectors is:…

Q: If A(つ2コ-1)っ B(3363-7)」cく2っろ」ー3)D(340-3)。 Calculate the angle between the veator Projection of ÁB…

A: Solution:-

Q: Find a unit vector that is perpendicular to both u = (1,0, 3) and v = (-1,2,0). Answer:

A: We have to find the unit vector which is perpendicular to given vectors.

Q: Consider the vectors u = (2,0) and v = (-4,4). Sketch the vectors, find the angle between the…

A: Click to see the answer

Q: 10- With respect to the origin O, the vertices of a triangle ABC have position vectors OA = 2i + 5k,…

A: (a) To show that triangle ABC is a right angled triangle, use scalar product of vector, that is…

Q: Given the vector u 2i + 1j, find the - magnitude and angle in which the vector points (measured…

A: Click to see the answer

Q: Find a unit vector orthogonal to both u and v. u = 31 - 2j - 5k V = +

A: Given vectors u = 3i -2j -5kv = 1/2i - 3/4j + 1/10k

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a –…

A: Click to see the answer

Q: Find the area of the parallelogram that had the given vectors as adjacent sides. Use a computer…

A: Click to see the answer

Q: Find the angle between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Knowledge Booster
Calculus
Learn more about
Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.
Recommended textbooks for you
  • Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781337278461
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
  • Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781305652224
    Author:Charles P. McKeague, Mark D. Turner
    Publisher:Cengage Learning
  • Linear Algebra: A Modern Introduction
    Algebra
    ISBN:9781285463247
    Author:David Poole
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781337278461
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra & Trigonometry with Analytic Geometry
    Algebra
    ISBN:9781133382119
    Author:Swokowski
    Publisher:Cengage
    Elementary Linear Algebra (MindTap Course List)
    Algebra
    ISBN:9781305658004
    Author:Ron Larson
    Publisher:Cengage Learning
    Algebra and Trigonometry (MindTap Course List)
    Algebra
    ISBN:9781305071742
    Author:James Stewart, Lothar Redlin, Saleem Watson
    Publisher:Cengage Learning
    Trigonometry (MindTap Course List)
    Trigonometry
    ISBN:9781305652224
    Author:Charles P. McKeague, Mark D. Turner
    Publisher:Cengage Learning