Question

if vector a,b and c are non-zero coplanar vectors,such that vector a.b=b.c=0. if a=1 and c=6 units. find the value of a.c? ​

Answer 1

$\vec{a}\cdot \vec{b}=\vec{b}\cdot\vec{c}=0$

All three vectors are coplanar.

a.b = 0

Thus, angle between a and b is 90

b.c = 0

Thus, angle between b and c is 90

a, b and c are coplanar

Therefore, Angle between a and c either 0 or 180

a.c = |a||c|cos(0) = 1*6*1 = 6

a.c = |a||c|cos(180) = 1*6*-1 = -6

|a.c|=|-6| = 6

Hence, The value of |a.c| = 6

Answer 2

Answer:

a ⋅ b = 0

b ⋅ c =0

All three vectors are coplanar.

a.b = 0

Thus, angle between a and b is 90

b.c = 0

Thus, angle between b and c is 90

a, b and c are coplanar

Therefore, Angle between a and c either 0 or 180

a.c = |a||c|cos(0) = 1*6*1 = 6

a.c = |a||c|cos(180) = 1*6*-1 = -6

|a.c|=|-6| = 6

Hence, The value of |a.c| = 6