Angle between line l and line m is 60degree

[ezsmith]

Homework Statement

The line l has the equation r= s(1,2,-1) and the line m has the equation r= (0,1,1)+t(5,a,5). Find the value of a such that the angle between the line l and m is 60degree.

The Attempt at a Solution

What I did was use the equation s(1,2,-1)xt(5,a,-5) = \sqrt{1^2 + 2^2 + 1^2}x\sqrt{5^2 + a^2 + 5^2} x cos 60

 

[HallsofIvy]

Yes, \vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta).
So \sqrt{6}\sqrt{50+ a^2}cos(60)= 10+ 2a
All you have to do is solve that equation for a. I recommend squaring both sides to get rid of the square root and solving the resulting quadratic equation.

 

[ezsmith]

Yes, \vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}|cos(\theta).
So \left(\sqrt{6}\sqrt{50+ a^2}cos(60)= 10+ 2a
All you have to do is solve that equation for a. I recommend squaring both sides to get rid of the square root and solving the resulting quadratic equation.

Yea finally I am able to solve it. I was having dilemma on the square root part but your advice had been really helpful. Thanks a lot HallsofIvy. Cheers
I got my answer a = \sqrt{30}. I accidentally put s(1,2,-1)xt(5,a,-5) when its suppose to be s(1,2,-1)xt(5,a,5) therefore its suppose to be 2a instead of 10+2a.