A particle moves from a point P to a point Q . The coordinates of point P are (3, -2, 4) and the displacement vector of the particle from P to Q is given by D = 2 i - 5 j + 4 k . The distance of point Q from the origin is:

Step-by-step solution

The position vector of point P is r _P = 3 i - 2 j + 4 k . The displacement vector from P to Q is given by D = r _Q - r _P . Rearranging this equation, the position vector of point Q is: r _Q = r _P + D r _Q = (3 i - 2 j + 4 k ) + (2 i - 5 j + 4 k ) r _Q = 5 i - 7 j + 8 k The distance of point Q from the origin is the magnitude of its position vector: | r _Q| = 5^2 + (-7)^2 + 8^2 | r _Q| = 25 + 49 + 64 = 138 Answer: 138