Mathematics - Vector Question with Solution | TestHub

Any four non-zero vectors in space are always linearly independent.

The area of a parallelogram with diagonals ${\vec{d}}_1=\hat{i}-2\hat{j}+\hat{k}$ and ${\vec{d}}_2=-\hat{i}+2\hat{j}-5\hat{k}$ is $2\sqrt{5}$.

$[\vec{a}\times \vec{b}\vec{b}\times \vec{c}\vec{a}]=(\vec{a}\cdot \vec{b})[\vec{a}\vec{b}\vec{c}]$ 。

The scalar projection of $\hat{i}+\hat{j}+\hat{k}$ on $-2\hat{i}+2\hat{j}+\hat{k}$ is $\frac{1}{3}$.