Question

The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz- plane at the point 0,172,-132 . Then;

• A. (A) a = 2, b = 8
• B. (B) a = 4, b = 6
• C. (C) a = 6, b = 4
• D. (D) a = 8, b = 6

Answer 1

Answer: (C)

(C) a = 6, b = 4

Answer 2

Explanation:
Given:The line passing through the points (5, 1, a) and (3, b, 1) crosses the yz- plane at the point 0,172,-132We have to find values of a, b.We know, Equation of Line in Symmetrical Form passing through points (x1, y1, z1) and (x, y, z) is given byx−x2x1−x2=y−y2y1−y2=z−z2z1−z2 ...(i)Thus, the equation of line passing through (5,1,a) and (3,b,1) isx−35−3=y−b1−b=z−1a−1since the line passes through the point (0,172,−132).∴ It satisfies equation (i),⇒0−32=172−b1−b=−132−1a−1⇒−32=17−2b2−2b=−152a−2...(ii)For −32=17−2b2−2b[ using (ii) ]⇒−6+6b=34−4b⇒10b=40⇒b=4010=4For −32=−152x−2[ using (ii) ]⇒−30=−6a+6⇒6a=36⇒a=366=6∴a=6,b=4Hence, the correct option is (C).