GATE 2020 AG – Question 36
A particle has $\mathbf R=(2t^3+4t^2)\mathbf i+(3t^2-5t)\mathbf j+(7t^2+6t)\mathbf k$. Find its velocity component along $3\mathbf i+2\mathbf j+\mathbf k$ at t=2.
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: (C) $168/\sqrt{14}$
Explanation
Differentiate position to obtain v=(6t²+8t,6t−5,14t+6). At t=2 this is (40,7,34). The specified direction has unit vector (3,2,1)/√14, so scalar projection=(120+14+34)/√14=168/√14, C.