Question

Write an unit vector parallel to (Vector A + Vector B)
Vector A = 2i cap + 3j cap
Vector B = i cap + 4j cap + 3k cap

Answer 1

The unit vector in the parallel direction of any vector u is given by

û = +/- (u/| u|)———————(1)

Magnitude of unit vector is always one.

Thus here unit vector in the parallel direction of sum of vectors is

sum of vectors= 3 i + 6 j - 2 k

Unit vector in the parallel direction of this vector would be obtained from (1)

+/-[(3 i + 6 j - 2 k)/|3 i + 6 j - 2 k|]

Since |3 i + 6 j - 2 k|

= sqr. root(3^2+6^2+ (-2)^2)

=sqr. root(9+36+4) = 7

Hence answer is

+/-[(3 i + 6 j - 2 k)/|3 i + 6 j - 2 k|]

=+/-[ (3 i + 6 j -2 k)/7]

= 3/7 i + 6/7 j - 2/7 k or -3/7 i - 6/7 j + 2/7 k