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Paper 1 · November 2010 · Vectors

The position vectors of the points $A$ , $B$ and $C$ relative to the origin $O$ are $a = 3i - j$ , $b = 2i + j + 3k$ and $c = i - j + 6k$ . Find the value of $a \cdot (b \times c)$ .

Model answer

36

Also accepted: +36

Explanation

a\cdot(b\times c)

is the determinant whose rows are

(3,-1,0)

,

(2,1,3)

and

(1,-1,6)

. Expanding along the top row,

3\big(1(6)-3(-1)\big)+1\big(2(6)-3(1)\big)+0 = 3(9)+1(9) = 36

.

Derived from ZIMSEC Further Mathematics 9187/1, November 2010, Q1

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