Quick questions on The scalar (dot) product explained: H2 Mathematics Vectors and Complex Numbers

5short Q&A pairs drawn directly from our worked dot-point answer. For full context and worked exam questions, read the parent dot-point page.

What is projection?

Show answer

The scalar projection of

\mathbf{a}

onto

\mathbf{b}

(the length of the shadow of

\mathbf{a}

along

\mathbf{b}

) is

\dfrac{\mathbf{a}\cdot\mathbf{b}}{|\mathbf{b}|}

. The vector projection multiplies this by the unit vector

\dfrac{\mathbf{b}}{|\mathbf{b}|}

to give a vector along

\mathbf{b}

What is sign of the angle?

Show answer

A negative dot product gives an obtuse angle (cosine negative); keep the sign through to the inverse cosine.

What is q1?

Show answer

Compute

\begin{pmatrix} 1 \\ 3 \\ -2 \end{pmatrix} \cdot \begin{pmatrix} 4 \\ -1 \\ 1 \end{pmatrix}

. [2 marks]

What is q2?

Show answer

Show that

\begin{pmatrix} 2 \\ 1 \\ 0 \end{pmatrix}

and

\begin{pmatrix} -1 \\ 2 \\ 5 \end{pmatrix}

are perpendicular. [2 marks]

What is q3?

Show answer

State the geometric meaning of

\mathbf{a}\cdot\mathbf{b} = 0

for non-zero vectors. [1 mark]

Have a question we have not covered?

This dot-point answer is short enough that we have not extracted many short questions yet. Read the full dot-point answer or ask Mo, our study assistant, in the chat for follow ups.

All MathsQ&A pages