Vectors and matrices › Lines, planes and vectors in space › Angles between vectors and planes

Cosine of angle between vectors

High school · ●●○○○ 20 pts

For certain vectors

\mathbf{p}

and

\mathbf{q}

, the vectors

3 \mathbf{p} + \mathbf{q}

and

5 \mathbf{p} - 3 \mathbf{q}

are orthogonal. Also, the vectors

2 \mathbf{p} + \mathbf{q}

and

4 \mathbf{p} - 2 \mathbf{q}

are orthogonal. If

\theta

is the angle between

\mathbf{p}

and

\mathbf{q}

, find

\cos \theta

. Give your answer as a decimal.

dot product orthogonal vectors vector norm angle between vectors