Question

if a vector,b vector,c vector a vector dot b vector is equal to a vector dot c vector prove that b vector is equal to c vector​

Answer 1

Answer:

Given, a = (b + c)

So, a, b and c are coplanar vectors.

We know, cross product of any two vectors generates a third vector which is perpendicular to both the vectors producing it.

Let, d = (b X c)

So, d must be perpendicular to both b and c.

So, d must be perpendicular to the plane containing vectors b and c.

Since, vectors a, b and c are coplanar; so, the plane containing vectors b and c, contains a as well.

So, vectors a and d are perpendicular to one another.

Also, we know, cos 90° = 0.

So, a . (b X c) = a . d = |a| * |d| * cos 90° = 0.