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Vectors · Question 47 of 125

What are the coordinates of D?

Question 47

MediumOriginal question

Three vertices of a parallelogram $ABCD$ , taken in order, are $A(1, 2, -1)$ , $B(2, -1, 0)$ and $C(5, 4, 3)$ .

What are the coordinates of $D$ ?

(6, 1, 4)

Correct answerYour answer

(-2, -3, -4)

Correct answerYour answer

(4, 7, 2)

Correct answerYour answer

(8, 5, 2)

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer C

Correct answer: C

In parallelogram $ABCD$ , $\overrightarrow{AD} = \overrightarrow{BC}$ , so $\vec{d} = \vec{a} + \vec{c} - \vec{b}$ .
$(1, 2, -1) + (5, 4, 3) - (2, -1, 0) = (4, 7, 2)$ .

Worth noting

$(6, 1, 4)$ is $\vec{b} + \vec{c} - \vec{a}$ , which makes $ABDC$ the parallelogram, with $BC$ as a diagonal.

Concept: A parallelogram by position vectors
Typical timeTypical: 120 s
Your timeYours: —

The rule this testsAddition, components and the section formula

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