Question

Show that the points A (1, 2, 7), B (2, 6, 3) and C(3, 10, -1) are collinear.

Answer 1

Answer:

Equate the direction..

Step-by-step explanation:

B - A = k(C - B)

Now subtract the x coordinate of A from B and equate ot with k(Coordinate of B from C)

X Coordinate. 2 - 1 = k(3 - 2)

If k exists and is real

Points are collinear....

Alternate method....

Solve the Determinant... of the Points

Alternate Method

$| 1 \: 2 \: 7 \\ 2 \: 6 \: 3 \\ 3 \: 10 \: - 1|$

Value Comes out to be zero... , Therefore points are collinear

Solving Determinant

1(6*-1 - 3*10) - 2(2*-1 - 3*3) + 7(2*10 - 6*3)

-36 + 22 + 14 = 0

Therefore Points are Collinear.

Two Methods...

Hope this helps you...