Question:
The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are
The values of p and q so that the line joining the points (7, p, 2) and (q, -2, 5) may be parallel to the line joining the points (2, -3, 5) and (-6, -15, 11) are
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Direction ratios of parallel lines must be proportional.
Updated On: Oct 1, 2026
- \(p = 4, q = -3\)
- \(p = 4, q = 3\)
- \(p = -4, q = 3\)
- \(p = -4, q = -3\)
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The Correct Option is B
Solution and Explanation
Step 1: Second line
Joining \((2,-3,5)\) and \((-6,-15,11)\) gives direction ratios \((-8,-12,6)\), proportional to \((4,6,-3)\).
Step 2: First line
Joining \((7,p,2)\) and \((q,-2,5)\) gives \((q-7,\ -2-p,\ 3)\).
Step 3: Proportion
Compare the \(z\) components: \(3 : 6 = \frac12\), so each component of the first is half of the corresponding one: \(q-7 = -4\) gives \(q = 3\), and \(-2-p = -6\) gives \(p=4\). Option (B).
Final Answer:
p = 4 and q = 3. \[ \boxed{\text{(B)}\ p=4,\ q=3} \]
Joining \((2,-3,5)\) and \((-6,-15,11)\) gives direction ratios \((-8,-12,6)\), proportional to \((4,6,-3)\).
Step 2: First line
Joining \((7,p,2)\) and \((q,-2,5)\) gives \((q-7,\ -2-p,\ 3)\).
Step 3: Proportion
Compare the \(z\) components: \(3 : 6 = \frac12\), so each component of the first is half of the corresponding one: \(q-7 = -4\) gives \(q = 3\), and \(-2-p = -6\) gives \(p=4\). Option (B).
Final Answer:
p = 4 and q = 3. \[ \boxed{\text{(B)}\ p=4,\ q=3} \]
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