System of linear and non-linear equations

[abdo799]

Homework Statement

find the vector with magnitude 5 and perpendicular to 3i-2j+4k and 4i-3j-k

The Attempt at a Solution

lets name the vector component x for the i y for the j and z for the k
i got three equation
1- x^2+y^2+z^2=25 ( magnitude)
2-3x-2y+4z=0
3-4x-3y-z=0 (2, 3 from dot product by the 2 given vectors)
i am supposed to solve those simultaneously, but i can't do it

 

[Dick]

Homework Statement

find the vector with magnitude 5 and perpendicular to 3i-2j+4k and 4i-3j-k

The Attempt at a Solution

lets name the vector component x for the i y for the j and z for the k
i got three equation
1- x^2+y^2+z^2=25 ( magnitude)
2-3x-2y+4z=0
3-4x-3y-z=0 (2, 3 from dot product by the 2 given vectors)
i am supposed to solve those simultaneously, but i can't do it

You could if you tried. Use equation 3 to solve for z in terms of x and y. Substitute that into equation 2 and solve for y in terms of x. Put it all into equation 1 and solve for x. But it would be a lot easier to use the cross product, if you know what that is.

 

[abdo799]

I tried it and it worked, thanks