Find the unit vector in the direction of 3i + 4j -12k

Question

Find the unit vector in the direction of \(3\hat i+4\hat j-12\hat k\).

Answer 1

Let the unit vector in the direction of \(\vec A=3\hat i+4\hat j-12\hat k\)

So any unit vector in the direction of \(\vec A=3\hat i+4\hat j-12\hat k\)

\(\vec B=\cfrac{\vec A}{|\vec A|}\)

So the magnitude of the vector \(|\vec A|=\sqrt{3^2+4^2+(-12)^2}\)

So, the unit vector

\(\hat B=\cfrac{3\hat i+4\hat j-12\hat k}{13}\)