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Three-Dimensional Geometry · Question 67 of 120

Question 67

MediumOriginal question

For which kk are the lines with direction ratios k,2,−1k, 2, -1 and 3,−1,43, -1, 4 perpendicular?

Options for question 67

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Perpendicular: 3k+2(−1)+(−1)(4)=03k + 2(-1) + (-1)(4) = 0.

  2. 3k=63k = 6, so k=2k = 2.

Worth noting

23\frac{2}{3} leaves out the last product, (−1)(4)(-1)(4).

Concept
Perpendicular lines
Typical time
90 s
Your time
—
The rule this testsThe angle between two lines
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Ten questions from Three-Dimensional Geometry, at your own pace.

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Ten questions from Three-Dimensional Geometry, at your own pace.

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