Vectors Proof Questions

50%

A vector diagram shows a triangle $O A B$ .

\vec{OA} = 2\mathbf{a}

\vec{OB} = 3\mathbf{b}

$P\,$ is the point on $AB\,$ such that $A P : P B = 1 : 4$

\vec{OP} = k(8\mathbf{a} + 3\mathbf{b})

Vector diagram of triangle OAB with OA equal to 2a, OB equal to 3b, P dividing AB in the ratio 1 to 4, and OP equal to k times 8a plus 3b.

Find the value of $k$ .

[4]

50%

A vector diagram shows a triangle $O A B$ .

\vec{OA} = 2\mathbf{a}

\vec{OB} = 3\mathbf{b}

$P\,$ is the point on $AB\,$ such that $A P : P B = 1 : 4$

\vec{OP} = k(8\mathbf{a} + 3\mathbf{b})

Vector diagram of triangle OAB with OA equal to 2a, OB equal to 3b, P dividing AB in the ratio 1 to 4, and OP equal to k times 8a plus 3b.

Find the value of $k$ .

[4]

Vectors Proof Questions Questions