7. Simplify: 5v+ 4u - 7(v - 2u) a) - 2v+2u b) - 2v + 6u c) 2v+18u d) 6v + 2u 8. Write OP = (-3, 1, 2) using standard unit vectors. a) 3x + y + 2z b) 3x + y + 2z c) - 3i + j + 2k d) 3i + j + 2k

Illustrate with an example and a diagram why a+b=6+a¯ for all vectors a and b

Express the vector -9-7x- 15x² as a linear combination of p₁ = 2 + x +4x², p₂ = 1- x + 3x² and p3 3 + 2x + 5x²

Evaluate the following vector expression: a = [3 -6 -2] -3 Calculate 3(ax + az) and enter your answer in the answer box below

2. Write 3 as a linear combination of the vectors +

Consider three vectorse A 6)-2k B 2+7)+k, C-3j + 5k (a) Find A (B+C) Fil A C) Find Ax (8+C) i Find Bx(A-C).

define (2a - b + 4c, 3a-c, 4b + c) as a linear combination of three nonzero vectors

Find all numbers a and b for which the vectors v = ai - 2j + k and w = bi + 2j + 2k are orthogonal and have the same magnitude. (Express numbers in exact form. Use symbolic notation and fractions where needed. Give your answer as a list of ordered pairs (a, b).) (a, b) = (1,2), (2,1) Incorrect

u = (7, -4), v = (2, 1) a) Calculate projvu. Leave in component form. b) Resolve u into u1 and u2. Leave in component form.