Question

Let $$\vec{a} = 3\hat{i} + 2\hat{j} + x\hat{k}$$ and $$\vec{b} = \hat{i} - \hat{j} + \hat{k}$$, for some real $$X$$. Then $$|\vec{a} \times \vec{b}| = r$$ is possible if:

A
332<r<532
B
0<r32
C
32<r332
D
r532

Solution

The correct option is C $$r \ge 5 \sqrt{\dfrac{3}{2}}$$$$\vec{a} \times \vec{b} = \begin{vmatrix}\hat{i}&\hat{j}&\hat{k} \\3&2 &x \\1&-1&1\end{vmatrix}$$$$= (2 +x)\hat{i} + (x - 3)\hat{j} - 5k$$$$|\vec{a} \times \vec{b}| = \sqrt{4 v+ x^2 + 4x + x^2 + 9 - 6x + 25}$$$$= \sqrt{2x^2 - 2x + 38}$$$$\Rightarrow |\vec{a} \times \vec{b}| \ge \sqrt{\dfrac{75}{2}}$$$$\Rightarrow |\vec{a} \times \vec{b}| \ge 5 \sqrt{\dfrac{3}{2}}$$Mathematics

Suggest Corrections

0

Similar questions
View More

People also searched for
View More