Three particles P, Q and R are moving along the vectors A = i + j B = j + k and C = -i + j respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector A and B. Similarly particle Q is moving normal to the plane which contains vector A and C. The angle between the direction of motion of P and Q is cos ⁻¹(1/√(x)). Then the value of x is _______________. Numerical answer type. Work it out, then open the answer.

Answer: 3. Direction of P: A × B = (i + j) × (j + k) = i - j + k. Direction of Q: A × C = (i + j) × (-i + j) = 2k. cos θ = ((i - j + k) · 2k)/(√(3) × 2) = 1/√(3) So x = 3.

Three particles P, Q and R are moving along the vectors A = i + j B =… | JEE Main 2021 (22 Jul, Shift 2)

Q13JEE Main 2021 · 22 JUL · SHIFT 2Difficult

Vector (Cross) Product

Three particles P, Q and R are moving along the vectors $\vec{A} = \hat{i} + \hat{j} \quad \vec{B} = \hat{j} + \hat{k}$ and $\vec{C} = -\hat{i} + \hat{j}$ respectively. They strike on a point and start to move in different directions. Now particle P is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B}$ . Similarly particle Q is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C}$ . The angle between the direction of motion of P and Q is $\cos^{-1}\left(\frac{1}{\sqrt{x}}\right)$ . Then the value of x is _______________.

Numerical answer type. Work it out, then open the answer.

Show answer and solution

Answer: 3

Direction of P: $\vec{A} \times \vec{B} = (\hat{i} + \hat{j}) \times (\hat{j} + \hat{k}) = \hat{i} - \hat{j} + \hat{k}$ .
Direction of Q: $\vec{A} \times \vec{C} = (\hat{i} + \hat{j}) \times (-\hat{i} + \hat{j}) = 2\hat{k}$ .
$\cos\theta = \frac{(\hat{i} - \hat{j} + \hat{k}) \cdot 2\hat{k}}{\sqrt{3} \times 2} = \frac{1}{\sqrt{3}}$
So $x = 3$ .

Report a mistake

Vector (Cross) Product question from JEE Main 2021 (22 Jul, Shift 2)

More questions on Vector (Cross) Product