Question

show that vector A.(vector B+vector C)=vector A.vectorB+vector A.vectorC)

Answer 1

Answer:

Let

A = a1 i + a2 j

B = b1 i + b2 j

We know A + B =A -B

substituting values of A & B in above equation we get

a1 i +a2 j +b1 i + b2 j =a1 i + a2 j -b1 i -b2 j

(a1+b1)i + (a2+ b2) j = (a1-b1)i +(a2-b2) j ….(I)

comparing i coeffecients of Equation (I) we get

a1+b1 = a1-b1 therefore b1 =0 is only solution for this.

similarly comparing j coefficients we get

a2+b2 = a2-b2 here also we get b2 = 0

hence B is a Zero Vector (B = 0).

Zero vector does not have a specific direction .

Hence Angle between above type of vectors is Indeterminable (Cannot be defined can be 0 degrees , 120 degrees 1.2453 degrees as zero vector does not have any specific angle