If the line segment joining the points A(7, p, 2) and B(q, -2, 5) be p

1.	If the line segment joining the points A(7, p, 2) and B(q, -2, 5) be parallel to the line segment joining the points C(2, -3, 5) and D(-6, -15,11), find the values of p and q.
Answer» Given: A(7, p, 2) and B(q, -2, 5), line segment joining these two points will be, AB = (q-7)i + (-2-p)j + 3k And the line segment joining C(2, -3, 5) and D(-6, -15, 11) will be, CD = -8i – 12j + 6k Then, the angle between these two line segments will be 0 degree. So, the cross product will be 0. AB x CD = 0 ((q-7)i + (-2-p)j + 3k) x ( -8i – 12j + 6k) = 0 Thus, solving this we get, p = 4 and q = 3

If the line segment joining the points A(7, p, 2) and B(q, -2, 5) be parallel to the line segment joining the points C(2, -3, 5) and D(-6, -15,11), find the values of p and q.

Answer»

Given: A(7, p, 2) and B(q, -2, 5), line segment joining these two points will be, AB = (q-7)i + (-2-p)j + 3k

And the line segment joining C(2, -3, 5) and D(-6, -15, 11) will be, CD = -8i – 12j + 6k

Then, the angle between these two line segments will be 0 degree. So, the cross product will be 0.

AB x CD = 0

((q-7)i + (-2-p)j + 3k) x ( -8i – 12j + 6k) = 0

Thus, solving this we get,

p = 4 and q = 3