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Three-Dimensional Geometry · Question 40 of 120

Question 40

MediumOriginal question

Which point lies on the line x−12=y−2−1=z+13\frac{x - 1}{2} = \frac{y - 2}{-1} = \frac{z + 1}{3}?

Options for question 40

Show the answer and explanation
CorrectNot quiteAnswer C

Correct answer: C

Explanation

  1. A point on the line is (1+2λ,2−λ,−1+3λ)(1 + 2\lambda, 2 - \lambda, -1 + 3\lambda).

  2. λ=2\lambda = 2 gives (5,0,5)(5, 0, 5); the others fit no single λ\lambda.

Worth noting

(2,−1,3)(2, -1, 3) is the direction, not a point of the line.

Concept
A point on a line
Typical time
90 s
Your time
—
The rule this testsThe equation of a line
Practise this chapter →

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

Practise this chapter →

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