Answer:
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
