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Vectors and matrices — Question 16

QCAA 2025, Paper 1 · 5 marks

Q16 · 2025 · Technology-freeComplex familiar5 marks

QUESTION 16 (5 marks)

A parallelepiped is a three-dimensional figure where all six faces are parallelograms. It can be defined by vectors

\mathbf a

,

\mathbf b

and

\mathbf c

, as shown. The origin

O

and points

P

,

Q

,

R

and

S

are vertices of the parallelepiped.

Use vectors

\mathbf a

,

\mathbf b

and

\mathbf c

to prove that the diagonal from

P

to

R

and the diagonal from

Q

to

S

bisect each other.

Parallelepiped defined by vectors a, b and c, with vertices O, P, Q, R and S labelled.

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