A⃗ is a vector quantity such that |A⃗| = non-zero constant. Which of the following expression is true for A⃗ ?

Solution

Physics sir · 4 steps

A vector makes zero angle with itself, and sin 0 = 0, so its cross product with itself vanishes.

1. Dot with itself. A⃗·A⃗ = |A⃗||A⃗|cos 0 = |A⃗|². Since |A⃗| is non-zero, this is positive, not zero.
2. Cross with itself. The angle between A⃗ and itself is 0, and the size of a cross product depends on sin θ.

   |A⃗×A⃗| = |A⃗||A⃗|sin 0 = 0

3. No sign for vectors. A cross product is a vector, so it cannot be "greater than" or "less than" zero. It can only equal the zero vector, and here it does.
4. So. A⃗×A⃗ = 0, which is option (c).

The idea to keep. Any vector crossed with itself, or with a vector parallel to it, gives the zero vector. A vector dotted with itself gives the square of its magnitude.

Answer from the NTA final answer key. Solution by PrepWiser.