In Exercises 1–2, find the length and direction (when defined) of u * v and v * u.
1. u =-8i - 2j - 4k, v = 2i + 2j + k
2. u = 3 /2 i - 1 /2 j + k, v = i + j + 2
Want to see the full answer?
Check out a sample Q&A here
Related Calculus Q&A
Find answers to questions asked by students like you.
Q: In Exercises 1–5, find the length and direction (when defined) of u * v and v * u. 1. u = 2i - 2j -…
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: Find the length and direction (when defined) of u x v and vxu. u= - 12i + 9j – 12k, v = - 4i + 3j –…
A: Using formula of u x v and v x u,
Q: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?
A: Given, vector u and v
Q: In Exercises 30–35 compute the indicated quantities when u = (−3, 1, −4), v = (2, 0, 5), and w =( 1,…
A: Given: u = (−3, 1, −4), v = (2, 0, 5), and w =( 1, 3, 13)
Q: Find the length and direction (when defined) of u x v and vxu. u= 5i + 3j – 5k, v=0
A: we know that uxv=|u|.|v|sin∅.n^where ∅ is angle between u and v and n^ is unit vector perpendicular…
Q: In Exercises 23–32, use the dot product to determine whether v and w are orthogonal. 23. v = i + j,…
A: 23). Given vectors are v=i+j and w=i-j. To determine whether given two vectors are orthogonal using…
Q: Show that except in degenerate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…
A: We will prove that (u*v)*w=(u.w)v-(v.w)u u*v=ijkuxuyuzvxvyvz…
Q: Find the length and direction (when defined) of u xv and vxu. u= - 12i + 8j – 20k, v = - 3i + 2j -…
A: Click to see the answer
Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where needed to give…
A: Given u→=4, 4, 2, v→=3, -1, -1
Q: (a) Prove that u + vand u - v are orthogonal in IR" if and only if ||u|| = ||v||. (b) Draw a diagram…
A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…
Q: Is it true that if x is orthogonal to v and w, then x is also orthogonal to v − w? Explain your…
A: Given that 'x' is orthogonal to 'v' and 'w' . This implies x,v=0and x,w=0
Q: Find the vector projection of b onto a when b =2i-4j+3 k, a 3i+j+2 k.
A: Given that: b=2i-4j+3ka=3i+j+2k
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: Find the length and direction (when defined) of u xv and v×u. u= - 8i – 4j – 3k, v = 3i + 3j + 4k
A: Click to see the answer
Q: Find u × v and show that it is orthogonal to both u and v.u = (−2, 1, 1), v = (4, 2, 0)
A: Click to see the answer
Q: Given vector u = (-1, –1) and v = (-1,1) , determine the value of 5v – u in component form.
A: A vector is a quantity with magnitude and direction. Given a coordinate system a vector can be…
Q: In Exercises 57-62, compute the angle between the two planes, defined asthe angle 0 (between O and…
A: Explanation: To find the angle between two planes, one has to find the angle between normal…
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: Compute the orthogonal projection of u onto v. Use the square root symbol 'V where needed to give an…
A: Click to see the answer
Q: Find the length and direction (when defined) of u x v. u = 2 i+ 2j- k, v = -i+ k
A: As per our guidelines we are supposed to answer only one question and rest of the questions are…
Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'V' where needed to give…
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: We'll answer the first question since the exact one wasn't specified . Please submit a new question…
Q: In Exercises 57-62, compute the angle between the two planes, defined asthe angle 0 (between O and…
A: to find the angle we will use the formula cosθ=A.B|A||B| (1) where A = <1, -3, 1>…
Q: Compute the orthogonal projection of u' onto v. Use the square root symbol 'V where needed to give…
A: We need to find orthogonal projection of u onto v.
Q: Find u × v and show that it is orthogonal to both u and v.u = (2, −3, 1), v = (1, −2, 1)
A: Click to see the answer
Q: Find the projection of u onto v and the vector component of u orthogonal to v for u = 3i − 5j + 2k…
A: Click to see the answer
Q: B) Given the vectors u = 7i+ 2j - k, v = 2i-3j - 6k. Find the projection o %3D u onto v.
A: Given u=7i+2j-k and v=2i-3j-6k We need to find the projection of u onto v
Q: Find u × v and show that it is orthogonal to both u and v. u = v =
A: Given u→=-1,0,7v→=8,-4,0
Q: Find u × v and show that it is orthogonal to both u and v.u = (4, 1, 0), v = (3, 2, −2)
A: Now cross product is,
Q: 10. Given two vectors u =6,2] and v = [-2,1), determine the projection of u on v.C %3D %3D
A: Click to see the answer
Q: Compute the orthogonal projection of u onto v. Use the square root symbol ' where needed to give an…
A: Click to see the answer
Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…
A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…
Q: In Rn with inner product{x, y} = xTyderive a formula for the distance between two vectorsx = (x1, .…
A: Take two vectors x and y in an inner product space x=x1,…,xn and y=y1,…,yn then x,y=xTy
Q: Find u × v and show that it is orthogonal to both u and v.u = (1, 1, 0), v = (0, 3, 0)
A: We have given; u = (1, 1, 0), v = (0, 3, 0)
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: Consider the following. u--8i-4j-2k, v - 4j + 4k (a) Find the projection of u onto v. (b) Find the…
A: Click to see the answer
Q: Consider the following. u--8i-4j-2k, v - 4j+4k (a) Find the projection of u onto v. (b) Find the…
A: Click to see the answer
Q: Assume that the vectors u = ai-j+k and w=i+9j+5k orthogonal. Then the are value of a is
A: If two vectors are orthogonal (perpendicular), then their dot product is 0. We use this to solve the…
Q: Assuming A (2,1,0 ) and B (3, -1, t) find the value of t such that the length of the vector AB is 3.
A: Click to see the answer
Q: Find r' (2), where r(t) = u(t) × v(t), with u(2) = (1, ,2, – 1), u' (2) = (3, ,0, 4) , and v(t) =…
A: Solution :-
Q: Compute the orthogonal projection of u onto v. Use the square root symbol 'v' where needed to give…
A: Click to see the answer
Q: Let U = (2,1,0), V = (1,0,1), and W = (2, −1,1). Find the plane through U, V, and W, expressed in…
A: Click to see the answer
Q: find the value of k for which the vectors u and v are orthogonal. u = 2i - kj v = 3i + 2j
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: What is the dependence on the following vectors: u=(3.0.1), v=(1,-1,0) and w=(1.0.1) thanks!
A: A set of vectors {v1,v2,...,vn} in Rn is said to be linearlyindependent if the vector equationx1v1 +…
Q: ir kümelerinden kaç tanesi R' için bir tabandır? how many of the given vector
A: A subest S of R2 is a subspace if and only if it contains the null vector whenever it contains two…
Q: 11. Find the volume of the parallelepiped determined by the vectors u = 2i + 3j - k, i + j - 2k ,…
A: Click to see the answer
Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…
A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w
Q: Calculate the scalar triple product u · (v × w), where u = (1, 1, 0),v = (3, −2, 2), and w = (4, −1,…
A: Click to see the answer
Q: Let u be the general A) Show that the general solution of the cable equation: with a > 0, is given…
A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…
