Question

The magnitude of parallel vectors (A vector and B vector ) are equal ?​

Answer 1

Answer:

 (a+b)×(a×b)

=a×(a×b)+b×(a×b)

=(a.b)a−(a.a)b+(b.b)a−(b.a)b

=(a.b)(a−b)+a−b       (b.b=b2=1,a.a=a2=1 as a.b are unit vectors)

=(a.b+1)(a−b)

=x(a−b),, where x=a.b+1 is a scalar.

∴ The given vector is parallel to a−b.

Answer 2

Explanation:

If two given vectors are said to be parallel, as shown in figure 1; then,

1. their magnitude remains the same, .i.e. |A| = |B|, where A and B are vector quantities.

2. their directions are the same

However, IF the directions are the same, and vectors A and B are as shown in figure 2, then magnitudes |A| ≠ |B|.

Bottom line:

For two given vectors parallel to each other, their directions are always the same, with θ= $0^{o}$.