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Three-Dimensional Geometry · Question 46 of 120

Which point lies on the line AB?

Question 46

MediumOriginal question

A line passes through A(2,−1,3)A(2, -1, 3) and B(4,3,−1)B(4, 3, -1).

Which point lies on the line ABAB?

Options for question 46

Show the answer and explanation
CorrectNot quiteAnswer D

Correct answer: D

Explanation

  1. Points of the line: (2+2t,−1+4t,3−4t)(2 + 2t, -1 + 4t, 3 - 4t).

  2. t=2t = 2 gives (6,7,−5)(6, 7, -5); each other option fails one coordinate.

Worth noting

(6,7,5)(6, 7, 5) gets xx and yy right for t=2t = 2 but adds 4t4t to zz instead of taking it away.

Concept
A point on a line in Cartesian form
Typical time
120 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.