ne Given vectors u and v, find (a) 3u (b) 3u + 2v (c) v-2u. ests (a) 3u (Type your answer in terms of i and j) nten ucce

a) u = (a) i + (b) j, so 3u = (3a) i + (3b) j.

b) u as in a), v = (c) i + (d) j, so 3u + 2v = (3a+2c) i + (3b+2d) j

c) v-2u = (c-2a) i + (d-2b) j

Step-by-step explanation:

Lets consider u = (a, b) and v = (c, d).

a) When a vector is multiplied by a constant, each element of the vector is multiplied by the constant.

So 3u = 3 (a, b) = (3a, 3b) = (3a) i + (3b) j.

b) First, we multiply both vectors by their respective constants.

3u = 3 (a, b) = (3a, 3b) = (3a) i + (3b) j.

2v = 2 (c, d) = (2c, 2d) = (2c) i + (2d) j.

Then, we add. When computing and addition between vector, we add the elements that are in the same position, i. e. (u+v) (1) = u (1) + v (1) ...

So 3u + 2v = (3a, 3b) + (2c, 2d) = (3a+2c, 3b+2d) = (3a+2c) i + (3b+2d) j

c)

v = (c, d)

-2u = (-2a, - 2b)

v-2u = (c-2a, d-2b) = (c-2a) i + (d-2b) j