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Vectors · Question 36 of 125

At which point do the diagonals of ABCD meet?

Question 36

EasyOriginal question

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

At which point do the diagonals of $ABCD$ meet?

(3, 3, 1)

Correct answerYour answer

(2, 1, 2)

Correct answerYour answer

(\frac{3}{2}, \frac{1}{2}, - \frac{1}{2})

Correct answerYour answer

(\frac{8}{3}, \frac{5}{3}, \frac{2}{3})

Correct answerYour answer

Show the answer and explanation

CorrectNot quiteAnswer A

Correct answer: A

The diagonals of a parallelogram bisect each other, so they meet at the midpoint of $AC$ .
$\frac{(1, 2, -1) + (5, 4, 3)}{2} = (3, 3, 1)$ .

Worth noting

$(2, 1, 2)$ halves $\vec{c} - \vec{a}$ ; the midpoint halves $\vec{a} + \vec{c}$ .

Concept: A parallelogram by position vectors
Typical timeTypical: 90 s
Your timeYours: —

The rule this testsAddition, components and the section formula

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