Answer: Projection of (2,6) onto (-1,5) is given by
\(\dfrac{28}{\sqrt{26}}\)
Step-by-step 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,
\(\mid b\mid=\sqrt{(-1)^2+(5)^2}\\\\\mid b\mid=\sqrt{1+25}\\\\\mid b \mid=\sqrt{26}\)
so, \(\dfrac{\vec{b}}{\mid b\mid}=\dfrac{-1\hat{i}+5\hat{j}}{\sqrt{26}}\)
Now, it becomes,
\(Projection=\dfrac{(2\ht{i}+6\hat{j}).(-1\hat{i}+5\hat{j})}{\sqrt{26}}\\\\Projection=\dfrac{-2+30}{\sqrt{26}}\\\\Projection=\dfrac{28}{\sqrt{26}}\)
Hence, projection of (2,6) onto (-1,5) is given by
\(\dfrac{28}{\sqrt{26}}\)
