Let u, v, w, z be vectors in R. (a) Compute the angle between 7 =...

 

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Let u, v, w, z be vectors in R. (a) Compute the angle between 7 = (-2, 1, 1) and w = (1, 1, -2). (2 points) (b) Let u, v, u be vectors such that 1 and u 1 w. Find a vector such that Z v, w but u Z. (1 point) (c) i. Prove that the sum of the squares of the length of the diagonals of a parallelogram equals the sum of the squares of the length of its sides. (2 points) y t u U-v u+v V X ii. Suppose , 7 R such that |||| = 3, || + v|| = 4 and ||- || 6. What number must |||| equal? (2 points) n (d) Let V, V2,..., Un E Rn such that i j for all i j and |||| = 1 for i = {1,...,n}. If = avi, compute ||||2. (3 points) Hint: Try first for n = 2, 3, then partial credits would be given in case a general attempt isn't successful! i=1 Let u, v, w, z be vectors in R. (a) Compute the angle between 7 = (-2, 1, 1) and w = (1, 1, -2). (2 points) (b) Let u, v, u be vectors such that 1 and u 1 w. Find a vector such that Z v, w but u Z. (1 point) (c) i. Prove that the sum of the squares of the length of the diagonals of a parallelogram equals the sum of the squares of the length of its sides. (2 points) y t u U-v u+v V X ii. Suppose , 7 R such that |||| = 3, || + v|| = 4 and ||- || 6. What number must |||| equal? (2 points) n (d) Let V, V2,..., Un E Rn such that i j for all i j and |||| = 1 for i = {1,...,n}. If = avi, compute ||||2. (3 points) Hint: Try first for n = 2, 3, then partial credits would be given in case a general attempt isn't successful! i=1

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a To determine the angle between two vectors For u and v you can apply the following formula cos cos ... View the full answer