What Is the Unit Vector Perpendicular to Both 4i - 3j + k and the z-Axis?

AI Thread Summary
To find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k, the vector must have a zero z-component. A vector is perpendicular to another if their dot product equals zero, which applies to both the given vector and the z-axis unit vector k. The cross product of the vector 4i - 3j + k and the z-axis unit vector will yield a vector perpendicular to both. The resulting vector can then be normalized to obtain a unit vector. This approach effectively addresses the problem of finding the desired unit vector.
Matt2k
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I'm sorry if this is placed under the wrong section of the forum.

But i really need help with a problem.

Well, here it is;

Find a unit vector that is parallel to the xy-plane and perpendicular to the vector 4i - 3j + k *note* there is a ^ above the ijk.
 
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Can you write down an algebraic condition for a vector to be parallel to the xy plane?
What about for a vector to be perpendicular to 4i-3j+k?
And for a vector to be a unit vector?
 
If the vector is parallel to the xy plane, it must be perpendicular to the z-axis. Unit vector k lies on the z-axis. So, if you find a vector that's perpendicular to both unit vector k and your vector, it will solve your problem.

Whenever you take the cross product of two vectors, the result is perpendicular to both of the original vectors.
 
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