Q113 / 180 · KCET 2022 · Mathematics

If $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$, then $|\mathbf{a}|$ is equal to

  • A
    9
  • B
    36
  • C
    4
  • Correct answer
    D
    2

Solution

Given, $|\mathbf{a} \times \mathbf{b}|+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$ Correct one is $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=36$ and $|\mathbf{a}|=3$ We know, $|\mathbf{a} \times \mathbf{b}|^2+|\mathbf{a} \cdot \mathbf{b}|^2=|\mathbf{a}|^2|\mathbf{b}|^2$ $$ \begin{array}{ll} \therefore & |\mathbf{a}|^2|\mathbf{b}|^2=36 \Rightarrow(3)^2|\mathbf{b}|^2=36 \\ \Rightarrow & |b|^2=4 \Rightarrow|b|=2 \end{array} $$ Hence, the correct option is (4).

Hence, the correct answer is option: 'D'.

Relevant Questions