Two particles A and B are moving with constant velocities. The velocity vector of particle A is given by v _A = 3 i + x j + 4 k (in m/s) and that of particle B is v _B = 4 i + 3 j + y k (in m/s). If both particles are

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Quantrex Academy · Accepted Answer

Correct answer: 12

Since the particles are moving with the same speed, the magnitudes of their velocity vectors are equal:

|\vec{v}_A| = |\vec{v}_B|

\sqrt{3^2 + x^2 + 4^2} = \sqrt{4^2 + 3^2 + y^2}

25 + x^2 = 25 + y^2

x^2 = y^2 \Rightarrow y = \pm x

Since the directions of motion are perpendicular, the dot product of their velocity vectors must be zero:

\vec{v}_A \cdot \vec{v}_B = 0

(3)(4) + (x)(3) + (4)(y) = 0

12 + 3x + 4y = 0

Case 1: If

y = x

12 + 3x + 4x = 0 \Rightarrow 7x = -12 \Rightarrow x = -\dfrac{12}{7}

This is rejected because it is given that

x > 0

.

Case 2: If

y = -x

12 + 3x + 4(-x) = 0

12 - x = 0 \Rightarrow x = 12

Thus, the value of

x

is 12.

Answer:

12

Two particles A and B are moving with constant velocities. The...

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