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

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» Line joining A (7, p, 2) and B (q, -2, 5) is written as AB = (q – 7) i + (- 2 – p) j + 3k Line joining C (2, -3, 5) and D (-6, -15, 11) is written as CD = -8i – 12j + 6k Here the angle between line segments is zero so the cross product is zero AB × CD = 0 Substituting the values ((q – 7) i + (-2 – p) j + 3k) × (- 8i – 12j + 6k) = 0 By solving the above equation 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»

Line joining A (7, p, 2) and B (q, -2, 5) is written as

AB = (q – 7) i + (- 2 – p) j + 3k

Line joining C (2, -3, 5) and D (-6, -15, 11) is written as

CD = -8i – 12j + 6k

Here the angle between line segments is zero so the cross product is zero

AB × CD = 0

Substituting the values

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

By solving the above equation we get

p = 4 and q = 3