Question

5. a) Suppose that the area of the parallelogram spanned by the vectors ~u and ~v...

5. a) Suppose that the area of the parallelogram spanned by the vectors ~u and ~v is 10. What is the area of the parallogram spanned by the vectors 2~u + 3~v and −3~u + 4~v ?

(b) Given (~u × ~v) · ~w = 10. What is ((~u + ~v) × (~v + ~w)) · ( ~w + ~u)? [4]

6. Find an equation of the plane that is perpendicular to the plane x + 2y + 4 = 0, contains the origin, and whose normal makes an angle of 30◦ with the z − axis.

Please answer both questions with detailed solution.

Homework Answers

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
In 3 dimensions, draw vectors u, v, w, and x such that u+v+w=x. The vectors u...
In 3 dimensions, draw vectors u, v, w, and x such that u+v+w=x. The vectors u and x share an initium. You may pick the size of your vectors. Make sure the math works. Find the angle between vector x and vector u.
1. Find the area of the parallelogram that has the given vectors as adjacent sides. Use...
1. Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer algebra system or a graphing utility to verify your result. u = 3, 2, −1 v = 1, 2, 3 3. Find the area of the triangle with the given vertices. Hint: 1 2 ||u ✕ v|| is the area of the triangle having u and v as adjacent sides. A(4, −5, 6), B(0, 1, 2), C(−1, 2, 0)
Find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1,...
Find the orthogonal projection of u onto the subspace of R4 spanned by the vectors v1, v2 and v3. u = (3, 4, 2, 4) ; v1 = (3, 2, 3, 0), v2 = (-8, 3, 6, 3), v3 = (6, 3, -8, 3) Let (x, y, z, w) denote the orthogonal projection of u onto the given subspace. Then, the components of the target orthogonal projection are
please answer all of them a. Suppose u and v are non-zero, parallel vectors. Which of...
please answer all of them a. Suppose u and v are non-zero, parallel vectors. Which of the following could not possibly be true? a) u • v = |u | |v| b) u + v = 0 c) u × v = |u|2 d) |u| + |v| = 2|u| b. Given points A(3, -4, 2) and B(-12, 16, 12), point P, lying between A and B such that AP= 3/5AB would have coordinates a) P(-27/5, 36/5, 42/5) b) P(-6, 8,...
5. Perform the following operations on the vectors u=(-4, 0, 2), v=(-1, -5, -4), and w=(0,...
5. Perform the following operations on the vectors u=(-4, 0, 2), v=(-1, -5, -4), and w=(0, 3, 4) u*w= (u*v)u= ((w*w)u)*u= u*v+v*w=
Let u and v be vectors in 3-space with angle θ between them, 0 ≤ θ...
Let u and v be vectors in 3-space with angle θ between them, 0 ≤ θ ≤ π. Which of the following is the only correct statement? (a) u × v is parallel to v, and |u × v| = |u||v| cos θ. (b) u × v is perpendicular to u, and |u × v| = |u||v| cos θ. (c) u × v is parallel to v, and |u × v| = |u||v|sin θ. (d) u × v is perpendicular...
(a) Find the volume of the parallelepiped determined by the vectors a =< 2, −1, 3...
(a) Find the volume of the parallelepiped determined by the vectors a =< 2, −1, 3 >, b =< −3, 0, 1 >, c =< 2, 4, 1 >. (b) Find an equation of the plane that passes through the point (2, 4, −3) and is perpendicular to the planes 3x + 2y − z = 1 and x − 2y + 3z = 4.
Let u, v, and w be vectors in Rn. Determine which of the following statements are...
Let u, v, and w be vectors in Rn. Determine which of the following statements are always true. (i) If ||u|| = 4, ||v|| = 5, and ?||u + v|| = 8, then u?·?v = 4. (ii) If ||u|| = 2 and ||v|| = 3, ?then |u?·?v| ? 5. (iii) The expression (v?·?w)u is both meaningful and defined. (A) (ii) and (iii) only (B) (ii) only (C) none of them (D) all of them (E) (i) only (F) (i) and...
1. Compute the angle between the vectors u = [2, -1, 1] and and v =...
1. Compute the angle between the vectors u = [2, -1, 1] and and v = [1, -2 , -1] 2. Given that : 1. u=[1, -3] and v=[6, 2], are u and v orthogonal? 3. if u=[1, -3] and v=[k2, k] are orthogonal vectors. What is the value(s) of k? 4. Find the distance between u=[root 3, 2, -2] and v=[0, 3, -3] 5. Normalize the vector u=[root 2, -1, -3]. 6. Given that: v1 = [1, - C/7]...
Let R4 have the inner product <u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4...
Let R4 have the inner product <u, v>  =  u1v1 + 2u2v2 + 3u3v3 + 4u4v4 (a) Let w  =  (0, 6, 4, 1). Find ||w||. (b) Let W be the subspace spanned by the vectors u1  =  (0, 0, 2, 1), and   u2  =  (3, 0, −2, 1). Use the Gram-Schmidt process to transform the basis {u1, u2} into an orthonormal basis {v1, v2}. Enter the components of the vector v2 into the answer box below, separated with commas.