Question

Looking for assistance on part (b) only for this question thank you!

Answer 1

Given:-

`<1,5>,<3,15>`

To find:-

The given vectors are parallel, orthogonal or neither.

So now we check, the given vectors is orthogonal or not.

`\begin{gathered} \bar{u}\bar{.v}=1(3)+5(15) \\ \text{ =3+75} \\ \text{ =78} \end{gathered}`

The given vectors are not orthogonal because if the vectors are orthogonal the dot product should be zero.

So now we check, the given vectors is parallel or not,

`\begin{gathered} \lvert u\rvert=\sqrt[]{1^2+5^2} \\ \text{ =}\sqrt[]{1+25} \\ \text{ =}\sqrt[]{26} \end{gathered}`

Also,

`\begin{gathered} \lvert v\rvert=\sqrt[]{3^2+15^2} \\ \text{ =}\sqrt[]{9+225} \\ \text{ =}\sqrt[]{234} \end{gathered}`

So now,

`\begin{gathered} \theta=\cos ^(-1)((u.v)/(\lvert u\rvert\lvert v\rvert)) \\ \theta=\cos ^(-1)(\frac{78}{\sqrt[]{26}\sqrt[]{234}}) \\ \theta=\cos ^(-1)((78)/(5.099*15.29)) \\ \theta=\cos ^(-1)(1) \\ \theta=90 \end{gathered}`

So we get the value of theta as 90 degree. So the given vectors are Parallel.