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. :)