Question

The points with position vectors 60i+3j,40i-8j,aj-52j are collinear if a is

Answer 1

Suppose, position vector A=60x+3j

position vector B=40i-8j

position vector C=aj-52j

Now, find vector AB and BC

AB= -20i-11j

BC= (a-40)i-44j

To be collinear,  angle between the vector AB and BC made by the given position vectors should be 0 or 180 degree.

That’s why the cross product of  the vectors should be zero

ABXBC=(-20i-11j)X(a-40)i-44j

0i+0j+(880+11(a-40))=0

a-40= -80

a=-40

Therefore, a should be -40 to be the given positions vectors collinear.

Answer 2

Answer:

Suppose, position vector A=60x+3j

position vector B=40i-8j

position vector C=aj-52j

Now, find vector AB and BC

AB= -20i-11j

BC= (a-40)i-44j

To be collinear,  angle between the vector AB and BC made by the given position vectors should be 0 or 180 degree.

That’s why the cross product of  the vectors should be zero

ABXBC=(-20i-11j)X(a-40)i-44j

0i+0j+(880+11(a-40))=0

a-40= -80

a=-40

Therefore, a should be -40 to be the given positions vectors collinear.

Step-by-step explanation: