Question 1

Paper 2Medium7 marks

A triangular inspection plate is fitted in a three-dimensional frame. From vertex OO the edges OAOA and OBOB are represented by the vectors

a=(2,1,2) m,b=(1,3,−1) m.\mathbf a=(2,1,2)\text{ m},\qquad \mathbf b=(1,3,-1)\text{ m}.

An engineer uses these edges to assess the size and orientation of the plate.

(a)

Determine the area of triangle OABOAB

[2]
(b)

Determine the acute angle between the lines OAOA and OBOB to the nearest 0.1∘0.1^\circ

[2]
(c)

Find the scalar component of a\mathbf a in the direction of b\mathbf b and the magnitude of the component of a\mathbf a perpendicular to b\mathbf b Give each answer to 3 significant figures.

[2]
(d)

Use your answers to part (c) to state whether OAOA is more nearly parallel or perpendicular to OBOB giving a reason.

[1]

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