Let three vectors a, b and c be such that... | Vector Algebra

JEE MAIN_2021_

22-JULY-2021,S2

Question

Let three vectors $\overline{\mathrm{a}}, \overline{\mathrm{b}}$ and $\overline{\mathrm{c}}$ be such that $\overline{\mathrm{a}} \times \overline{\mathrm{b}}=\overline{\mathrm{c}}, \overline{\mathrm{b}} \times-\overline{\mathrm{c}}=\overline{\mathrm{a}}$ and $|\overline{\mathrm{a}}|=2$. Then which one bf the following is not trues?

Select the correct option:

$\overline{\mathrm{a}} \times((\overline{\mathrm{b}} \times \overline{\mathrm{c}}) \times(\overline{\mathrm{b}}-\overline{\mathrm{c}}))=\overline{0}$

Projection of $\bar{a}$ on $(\bar{b} \times \bar{c})$ is 2

$[\overline{\mathrm{a}} \overline{\mathrm{b}} \overline{\mathrm{c}}]+[\overline{\mathrm{c}} \overline{\mathrm{a}} \overline{\mathrm{b}}]=8$

$|3 \bar{a}+\bar{b}-2 \bar{c}|^2=51$

✓ Correct! Well done.

✗ Incorrect. Try again or view the solution.

Solution