Question

If vector a = 2i + 3j - 4k, vector b = 3i - 4j - 5k and vector c = -3i + 2j + 3k, find the magnitude and direction cosines of

(i) vector (a + b + c)

(ii) vector (3a - 2b + 5c)

Answer 1

Given vector a = 2i + 3j - 4k, vector b = 3i - 4j - 5k and vector c = -3i + 2j + 3k

(i) vector (a + b + c) = 2i + j - 6k

|vector(a + b + c)| = √(4 + 1 + 36) = √41

D.c's of vector (a + b + c) = (2/√41,1/√41,-6/√41)

(ii) vector (3a - 2b + 5c)