Let L be the foot of the perpendicular drawn from the point P(5, 3k-7, -4) to the YZ-plane. If the distance of point L from the origin is 41 units, then the possible value of ' k ' is:

Step-by-step solution

The coordinates of the foot of the perpendicular L from the point P(5, 3k-7, -4) to the YZ-plane are obtained by setting its x-coordinate to zero. Thus, L = (0, 3k-7, -4) . The distance of L from the origin is given as 41 . 0^2 + (3k-7)^2 + (-4)^2 = 41 Squaring both sides, we get: (3k-7)^2 + 16 = 41 (3k-7)^2 = 25 3k-7 = 5 Taking the positive sign: 3k-7 = 5 3k = 12 k = 4 Taking the negative sign: 3k-7 = -5 3k = 2 k = 2 3 From the given options, the possible value of k is 4 . Answer: 4