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 vectors ⃗A and ⃗B. Similarly particle Q is moving normal…

Question

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 vectors ⃗A and ⃗B. Similarly particle Q is moving normal to the plane which contains vectors ⃗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 .

Accepted Answer

3. Normal to the plane of ⃗A, ⃗B: ⃗A×⃗B = (̂i + ̂j)×(̂j + ̂k) = ̂i - ̂j + ̂k. Normal to the plane of ⃗A, ⃗C: ⃗A×⃗C = (̂i + ̂j)×(-̂i + ̂j) = 2̂k. cos θ = ((1)(0) + (-1)(0) + (1)(2))/(√3·2) = 1/(√3), so x = 3.

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