Question

Find the direction cosines of the vector joining the points A (1, 2, -3) and B(-1, -2, 1), directed from A to B.

Answer 1

Vector a = 1i + 2j - 3k  or (1, 2, -3)

b = -i -2j + k or (-1, -2, 1)

now, ab =  (-1 - 1)i + (-2 - 2)j + (1 - (-3)) k

ab = -2i - 4j + 4k

Therefore, magnitude of vector ab = √(-2)² + (-4)² + (4)²

= √36

= 6

Now, if there is an vector X = ai + bj + ck, then

Direction cosines = a/|X| , b/|X|, c/|X|,

Using this formula only,

we get,

Direction cosines = (-2/6 , -4/6, 4/6)

= (-1/3, -2/3 , 2/3)

Hope it helps.