Question

find values of A and B so that the points (a,b,3), (2,0,-1), and (1,-1,3) are collinear

Answer 1

Answer:

a = 1 and

b = -1

Step-by-step explanation:

If the points X(a, b, 3), Y(2, 0,−1) & Z(1, -1 ,3) are collinear in 3D plane.  

then XY = (a – 2)i + (b – 0)j + (3 + 1)k must be parallel to  

YZ = (2 – 1)i + (0 + 1)j + (-1 -3)k

XY = (a-2)i + bj + 4k  

YZ = i + j -4k

Hence the ratios of corresponding direction ratios of must be equal hence

(a -2)/1 = b/1 = 4/-4

Solving above equations, we get  

a – 2 = -1

a = 1 and

b = -1

Answer 2

Answer:

Step-by-step explanation:

If the points X(a, b, 3), Y(2, 0,−1) & Z(1, -1 ,3) are collinear in 3D plane.  

then XY = (a – 2)i + (b – 0)j + (3 + 1)k must be parallel to  

YZ = (2 – 1)i + (0 + 1)j + (-1 -3)k

XY = (a-2)i + bj + 4k  

YZ = i + j -4k

Hence the ratios of corresponding direction ratios of must be equal hence

(a -2)/1 = b/1 = 4/-4

Solving above equations, we get  

a – 2 = -1

a = 1 and

b = -1