Question

What is the projection of (4 4) onto (-7 3) open study?

Answer 1

Write the two vectors as

`\vec{a} =4\vec{i} + 4\vec{j}`

`\vec{b} = -7\vec{i}+3\vec{j}`

By definition, the projection of
`\vec{a}` onto
`\vec{b}` is

`a_(b) = \vec{a} . \frac{\vec{b}}b`


`\hat{b} = \frac{\vec{b}}b = (1)/(√(49+9)) (-7\vec{i}+3\vec{j})=(-7\vec{i}+3\vec{j})/√(58)`

Therefore

`\vec{a} . \vec{b} = -28+12=-16`

`a_(b) = -16/√(58) = -2.1`

Answer:
The projection of (4 4) onto (-7 3) is -2.1.