Question about vectors. help!!!!?

Question

Find the vectors that satisfy the stated conditions.

Part 1. Same directions as v = -2i + 3j and three times the length of v.

Part 2. Length 2 and oppositely directed to v = -3i + 4j + k.

Answer 1

1.

Let V be the new vector.

Multiply each component v by 3:

V = - 6i + 9j.

2.

The length of v is:

sqrt((- 3)^2 + 4^2)

= 5.

The vector V of length 2 in the same direction is 2v / 5, and in the opposite direction is:

V = - 2v / 5 = 6i / 5 - 8j / 5 - 2k / 5.