Question:
If the line through the points A(k,1,-1) and B(2k,0,2) is perpendicular to the line through the points B and C(2+2k,k,1), then the value of k is
If the line through the points A(k,1,-1) and B(2k,0,2) is perpendicular to the line through the points B and C(2+2k,k,1), then the value of k is
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Perpendicular lines have zero dot product of direction vectors.
Updated On: Mar 20, 2026
- \(-1\)
- \(1\)
- \(-3\)
- 3
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The Correct Option is A
Solution and Explanation
Direction vectors:
vecAB=(k, -1, 3), vecBC=(2, k, -1).
Perpendicular ⟹ vecAB·vecBC=0:
2k+k(-1)-3=0⟹ k=-1.
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