Question

Which of the following vectors is parallel to v = i + 2j?

A w = -i - 2j
B w = i - 2j
C w= i + j
D w = 2i + 2j

Answer 1

Multiply A by -1 and one has w = i + 2 j which is parallel and in the 2 opposite direction,

Also tan theta = 2 / 1 = 2

This is also the tan for vector A but in the third quadrant

Answer 2

The vector w = 2i + 4j is parallel to the vector v = i + 2j because it is a scalar multiple of v, with none of the other options being scalar multiples of v.

Step-by-step explanation:

The vector v = i + 2j is parallel to another vector when that vector is a scalar multiple of v. Looking at the given options, the vector w = 2i + 4j is the one that is parallel to v because it can be obtained by multiplying the original vector by a scalar (in this case, the scalar is 2). None of the other given vectors is a scalar multiple of v. Specifically, vector w = -i - 2j is antiparallel (parallel but in the opposite direction) to v, vector w = i - 2j is not parallel because the j-component has a different sign, and vector w = i + j does not have the same ratio between i and j components as v.