Use vectors to prove that in `triangleABC` : `c=acos B+bcos A`.

Use vectors to prove that in triangleABC : a=bcos C+c cos B .

Use vectors to prove that in triangleABC : b=c cos A+a cos C .

Using vector method, prove that the angel in a semi circle is a right angle.

Using vector, prove that sin(A+B)=sinAcosB+cosAsinB

State Polygon law of vector addition and prove it using Triangle law of vector addition.

In a triangleABC , if |(1,1,1),(1+sinA,1+sinB,1+sinC),(sinA+sin^2A,sinB+sin^2B,sinC+sin^2C)|=0 , then prove that triangleABC is an isosceles triangle.

In any triangle ABC, then by vectors, prove that : a=b cos C+c cos B .

Using vectors, prove that a parallelogram whose diagonals are equal is a rectangle.

In Fig., ABC and AMP are two right triangles, right angled at B and M respectively. Prove that: (i) triangleABC ~ triangleAMP (ii) (CA)/(PA) = (BC)/(MP)