Question

If vector a = 2i - j + 2k and vector b = -i + j - k, find a unit vector in the direction of vector(a + b).

Answer 1

Answer:

A vector perpendicular to both "a" and "b" is

b×a = 9i +8j + 14k

However, this vector has a magnitude of √341 ≈ 18.4661...; clearly, not an unit vector. The unit vector you seek is thus

9i + 8j + 14k

--------------- ≈ .48738i + .43322j + .75814k

√341

For a check, compute the sum of the squares of the above figures; it should amount to 1.