Question

if |A*B| =3A.B then the value of |A+B| is

Answer 1

|AB|= 3A.B
|AB| = 3|A |.| B | cos∅ wABhere ∅ is angle between a and b .
|AB| = 3|AB|cos∅
1 = 3cos∅
cos∅ = 1/3 -------(1)

| A + B | = √{A² + B² + 2|A|.|B|.cos∅}
= √{A² + B² + 2|A|.|B|.×1/3 }
when , A and B are unit vectors .
= √{ 1 + 1 + 2 × 1/3 }
= 2√2/3

Answer 2

A and B are vectors.

LHS = | A × B | = A B Sin theta
it is the cross product.
RHS = 3 | A · B | = 3 A B cos theta
It is the dot product.
So sin theta = 3 cos theta
Tan theta = 3.
Sec^2 theta = 10
Cos theta = sqrt(10).

| A + B | = C
|C|^2 = A^2 + B^2 + 2 A B sqrt(10)