Assertion (A): The lines with direction ratios $3, -1, 2$ and $1, 1, -1$ are perpendicular.
Reason (R): Two lines are perpendicular when their direction ratios are proportional.

Both A and R are true, and R is the correct explanation of A.Correct answerYour answerBoth A and R are true, but R is not the correct explanation of A.Correct answerYour answerA is true, but R is false.Correct answerYour answerA is false, but R is true.Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

A: $3(1) + (-1)(1) + 2(-1) = 0$ , so A is true.
R is false: proportional ratios make lines parallel; perpendicular lines need $a_1a_2 + b_1b_2 + c_1c_2 = 0$ .

Concept: Parallel and perpendicular lines
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe angle between two lines

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

Assertion (A): The lines with direction ratios 3,−1,23, -1, 23,−1,2 and 1,1,−11, 1, -11,1,−1 are perpendicular.Reason (R): Two lines are perpendicular when their direction ratios are proportional.

Explanation

Assertion (A): The lines with direction ratios $3, -1, 2$ and $1, 1, -1$ are perpendicular.
Reason (R): Two lines are perpendicular when their direction ratios are proportional.