Find Values of a and b for Perpendicular Vectors

[noahsdev]

Homework Statement

If $\underline{v}$ = a$\underline{i}$ + 2$\underline{j}$ + 3$\underline{k}$ and $\underline{w}$ = 2$\underline{i}$ +b$\underline{j}$ - $\underline{k}$ and |$\underline{v}$| = |$\underline{w}$|, find the values of a and b so that $\underline{v}$ and $\underline{w}$ are perpendicular.

If v = ai+3j+3k and w = 2i+bj-k and |v| = |w|, find the values of a and b so that v and w are perpendicular.

Homework Equations

$\underline{a}$ - ($\underline{a}$.$\underline{\hat{b}}$)$\underline{\hat{b}}$

The Attempt at a Solution

sqrt(a²+13) = sqrt(b²+5)

I am so confused right now. Any help would be great. Thanks

 

[Mark44]

Homework Statement

If $\underline{v}$ = a$\underline{i}$ + 2$\underline{j}$ + 3$\underline{k}$ and $\underline{w}$ = 2$\underline{i}$ +b$\underline{j}$ - $\underline{k}$ and |$\underline{v}$| = |$\underline{w}$|, find the values of a and b so that $\underline{v}$ and $\underline{w}$ are perpendicular.

Homework Equations

$\underline{a}$ - ($\underline{a}$.$\underline{\hat{b}}$)$\underline{\hat{b}}$

The Attempt at a Solution

sqrt(a²+13) = sqrt(b²+5)

I am so confused right now. Any help would be great. Thanks

That's one equation. To get another equation, use the requirement that u and v be perpendicular. Hint: There is a simple operation that can be used to determine whether two vectors are perpendicular.

 

[noahsdev]

That's one equation. To get another equation, use the requirement that u and v be perpendicular. Hint: There is a simple operation that can be used to determine whether two vectors are perpendicular.

Thanks, haha, so simple. I'm so angry at myself now. :)