Question

What is the projection of (2,6) onto (-1,5)?

Answer 1

Answer: Projection of (2,6) onto (-1,5) is given by

`(28)/(√(26))`

Explanation:

Let
`\vec{a}=2\hat{i}+6\hat{j}`

and
`\vec{b}=-1\jhat{i}+5\hat{j}`

we need to find the projection of
`\vec{a}` onto
`\vec{b}`

As we know the formula for projection:

`Projection=\frac{\vec{b}}{\mid b\mid}. \vec{a}`

Since we know the value of
`\vec{b}=-1\jhat{i}+5\hat{j}`

so,

`\mid b\mid=√((-1)^2+(5)^2)\\\\\mid b\mid=√(1+25)\\\\\mid b \mid=√(26)`

so,
`\frac{\vec{b}}{\mid b\mid}=\frac{-1\hat{i}+5\hat{j}}{√(26)}`

Now, it becomes,

`Projection=\frac{(2\ht{i}+6\hat{j}).(-1\hat{i}+5\hat{j})}{√(26)}\\\\Projection=(-2+30)/(√(26))\\\\Projection=(28)/(√(26))`

Hence, projection of (2,6) onto (-1,5) is given by

`(28)/(√(26))`

Answer 2

1.08(-1,5)

Explanation:

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