3D Orthogonal Vectors with unknown Components:
Find the value of x such that a and b are orthogonal,
where a = 3i + 2j + xk, and b = -2i - 4j + xk.
If two vectors are orthogonal, the angle between them is 90° , making the cosine of the angle between them 0.
Hence, we proceed by finding the value of x which makes the cosine 0:
. Here this becomes
. We need to solve only the numerator:
The two vectors must have a 90° angle between them.