Question

True or False

Given two nonzero vectors vand w, it is always possible to decompose v into two vectors, one parallel to w and the other perpendicular to w.

Short answer

The given statement is True.

Step-by-step solution

Step 1. Given Information  

We are given an incomplete statement about the dot product.

We have to find whether the given statement is true or false.

Step 2. Finding True or False

Any two nonzero vectors v and w can be decomposed into two vectors, if they are having the same initial point. One of these will be parallel to w and the other one will be orthogonal to w.

Hence the given statement is True.