Question

Find a unit vector perpendicular to each of the vectors a + 2b and vector(2a + b), where  vector a = 3i + 2j + 2k and vector b = i + 2j - 2k.

Answer 1

Given that vector a = 3i + 2j + 2k and vector b = i + 2j - 2k

∴ vector(a + 2b) = 3i + 2j + 2k + 2(i + 2j - 2k)

= 3i + 2j + 2k + 2i + 4j - 4k = 5i + 6j - 2k

and 2a + b = 2(3i + 2j + 2k) + i + 2j - 2k

= 6i + 4j + 4k + i + 2j - 2k = 7i + 6j + 2k

Now, perpendicular vector of vector a + 2b and vector(2a + b)