In Exercises 1–3, 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 _{v}u.

1. v = 5j - 3k, u = i + j + k

2. v =-i + j, u = sqrt(2)i + sqrt(3)j + 2k

3. v = 5i + j, u = 2i + sqrt(17)j

### Want to see the full answer?

Check out a sample Q&A here*arrow_forward*Check out a sample Q&A here

*star_border*

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

A: 1.Given vectors are

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: 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: 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: 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: 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: 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,…

*question_answer*

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…

*question_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…

*question_answer*

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…

*question_answer*

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

*question_answer*

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…

*question_answer*

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.

*question_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

*question_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

*question_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

*question_answer*

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

*question_answer*

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

*question_answer*

Q: Evaluate 1+ x2 + y?dS, where S is the nelicoid with vector equation (u, v) 0 < u< 2, 0

A: Click to see the answer

*question_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…

*question_answer*

Q: In Exercises 14–17, find (a) the displacement vectors from r(a) to r(b), (b) the magnitude of the…

A: Take the displacement function, rt=t,t2; a=2, b=3 (a) Substitute 2 for a and 3 for b respectively…

*question_answer*

Q: What are the possible angles θ between two unit vectors e and f if ||e × f|| = 1/2 ?

A: The cross product of two vectors can be found by the formula a→×b→=a→b→sinθ The magnitude of the…

*question_answer*

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

*question_answer*

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

*question_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

*question_answer*

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:-

*question_answer*

Q: Find the unit Vector e(subv) where v=(2,2,1)ev=?I appreciate the help in advance

A: Formula used:Unit vector in direction v is

*question_answer*

Q: c) What is the cosine of the angle between the planes x + 2y – z + 1 = 0, and -x+ 3z + 1= 0? d) Find…

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

*question_answer*

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.

*question_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.

*question_answer*

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…

*question_answer*

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

*question_answer*

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

*question_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

*question_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.

*question_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…

*question_answer*

Q: 24. Verify the parallelogram law for vectors u and v in R": |u + v|l° + |[u – v||² = 2||u||² +…

A: Click to see the answer

*question_answer*

Q: Verify the Pythagorean Theorem for the vectors u and v.u = (3, −2), v = (4, 6)

A: Click to see the answer

*question_answer*

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

*question_answer*

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.

*question_answer*

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

*question_answer*

Q: i) Find a vector x with magnitude 3 that is in opposite direction to u. ii) Determine whether u and…

A: Click to see the answer

*question_answer*

Q: 10. Find the unit vector in the direction of u=2i+3j-k

A: Magnitude of u = sqrt (u1^2 + u2^2 + u3^2) Unit vector direction of d => u/ (Magnitude of u)…

*question_answer*

Q: Find the angle θ between the vectors.u = (1, 1, 1), v = (2, 1, −1)

A: The vectors are To find the angle between the given vectors, use formula

*question_answer*

Q: Determine the work done in moving a particle from P to Q when the magnitude and direction of the…

A: Click to see the answer

*question_answer*

Q: what is u.v when u and v are two unit vectors with an angle of (pi/6) between them. if u=i and if v…

A: Given: u=i, angleθ between u and v=π6 let's assume v=xi+yjx2+y2 we know that angle between two given…

*question_answer*

Q: Find a unit vector orthogonal to both u and v. u = i + 2j + 2k v = 2i +j – 2k

A: Click to see the answer

*question_answer*

Q: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v