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Three-Dimensional Geometry · Question 36 of 120

What are the coordinates of M?

Question 36

EasyOriginal question

A point $P(5, 1, 4)$ and the line $L: \frac{x - 1}{2} = \frac{y}{2} = \frac{z - 3}{-1}$ are given. $M$ is the point of $L$ with parameter $\lambda$ , and $F$ is the foot of the perpendicular from $P$ to $L$ .

What are the coordinates of $M$ ?

(1 + 2\lambda, 2\lambda, 3 - \lambda)

Correct answerYour answer

(2 + \lambda, 2, -1 + 3\lambda)

Correct answerYour answer

(1 + 2\lambda, 2\lambda, 3 + \lambda)

Correct answerYour answer

(-1 + 2\lambda, 2\lambda, -3 - \lambda)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Set each fraction equal to $\lambda$ : $x - 1 = 2\lambda$ , $y = 2\lambda$ , $z - 3 = -\lambda$ .
So $M = (1 + 2\lambda, 2\lambda, 3 - \lambda)$ .

Worth noting

$(2 + \lambda, 2, -1 + 3\lambda)$ swaps the point $(1, 0, 3)$ and the direction $2, 2, -1$ .

Concept: The foot of the perpendicular from a point to a line
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsThe equation of a line

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