Vectors I: scalar and vector products

Question code: bbb7A2CG746C32

Question 1103

Referred to the origin

{O,}

the position vectors of the points

{A}

and

{B}

are

7 \mathbf{i} - \mathbf{j} + 2 \mathbf{k} \quad \textrm{ and } \quad - 3 \mathbf{i} - 7 \mathbf{j} + 7 \mathbf{k}

respectively.

Show that

{OA}

and that

{OB}

are perpendicular.

Find the position vector of the point

{V}

{AB}

extended such that

{AB:AV = 3:5.}

The point

{C}

has position vector

{4 \mathbf{i} + 6 \mathbf{j} - 3 \mathbf{k}.}

Use a vector product to find the exact area of triangle

{OBC}

Answer

{\frac{1}{3} ( - 29 \mathbf{i} - 33 \mathbf{j} + 31 \mathbf{k} )}

{\frac{1}{2} \sqrt{902}}

Question code: bbb7A2CG746C32