Question

Could someone please help me with this question.
The points A (-2, -1, z) B (2, 4, 3) and C (10, y, -1) are collinear. Find the values of y and z.

Answer 1

I've got a neater way to do this, if you allow.

If ABC are collinear, then the area of \(\triangle ABC\) is zero.

Answer 2

Do you know what the formula of the area of a triangle is given three points?

Answer 3

Otherwise, just try vectors, which I think @ganeshie8 is proficient in.

Answer 4

that area method works too, vectors method is also nice

Answer 5

ah alright thx

Answer 6

AB = (4, 5, 3-z)
BC = (8, y-4, -4)

for AB and BC to be in same direction, the components must be proportional :
\[\large \dfrac{4}{8} = \dfrac{5}{y-4} = \dfrac{3-z}{-4}\]

solve y,z

Answer 7

let me know if that not clear enough