Question

find the direction cosines of the vector joining the two points (4,2,2,) & (7,6,14)

(this is new to me, used to think it was just one point not two.)

Answer 1

change in x = 7 - 4 = 3
change in y = 6 - 2 = 4
change i z = 14 - 2 = 12
so V = 3 i + 4 j + 12 k is in the direction

magnitude:
sqrt (9+16+144) = 13

dot product with unit x vector for example
V dot 1 i = 13 * 1 * cos angle
so
cos angle = 3/13
then y axis
cos angle = 4/13
and x
cos angle = 12/13

Answer 2

in the text book, the answer is -2i -7j -18k . could it be a mistake has being made? i mean your result or the one from the text

Answer 3

I thinks the one on the textbook is correct but why are you doing change in x,y&z