Which of these sets of three points is collinear?

(1, 2, 3), (3, 0, 5), (4, -1, 6)

Correct answerYour answer

(1, 1, 1), (2, 3, 2), (4, 7, 5)

Correct answerYour answer

(0, 0, 0), (1, 2, 3), (2, 3, 4)

Correct answerYour answer

(2, 1, 0), (0, 3, 2), (-2, 5, 3)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

Three points $A$ , $B$ , $C$ are collinear when $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are parallel, with components in one ratio.
For $(1, 2, 3), (3, 0, 5), (4, -1, 6)$ : $\overrightarrow{AB} = 2\hat{i} - 2\hat{j} + 2\hat{k}$ and $\overrightarrow{AC} = 3\hat{i} - 3\hat{j} + 3\hat{k} = \frac{3}{2}\overrightarrow{AB}$ .

Worth noting

In $(1, 1, 1), (2, 3, 2), (4, 7, 5)$ the $\hat{i}$ and $\hat{j}$ parts of $\overrightarrow{AB}$ and $\overrightarrow{AC}$ are in the ratio 3, but the $\hat{k}$ parts are not.

Concept: Collinear points
Typical timeTypical: 90 s
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The rule this testsAddition, components and the section formula

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Ten questions from Vectors, at your own pace.

Which of these sets of three points is collinear?

Explanation