JEE Main 2021 · 22 July · evening · Single correct · +4 / −1

Let three vectors a⃗, b⃗ and c⃗ be such that a⃗ × b⃗ = c⃗, b⃗ × c⃗ = a⃗ and | a⃗ | = 2. Then which one of the following is not true?

1. (a) a⃗ × ( (b⃗ + c⃗ ) × (b⃗ × c⃗ ) ) = 0⃗
2. (b) Projection of a⃗ on (b⃗ × c⃗ ) is 2
3. (c) [ a⃗, b⃗, c⃗ ] + [ c⃗, a⃗, b⃗ ] = 8
4. (d) | 3a⃗ + b⃗ - 2c⃗ |² = 51