If A.B=6 and |A×B|=8, then AB is . . .

Question : If A.B=6 and |A×B|=8, then AB is  (a) 2 (b) 10 (c) 14 (d) 48

Doubt by Rohan

Solution :

A.B=6 ABcosθ=6 — (1)

|A×B|=8

ABsinθ=8—(2)

Dividing equation (2) by (1)

ABsinθ/ABcosθ = 8/6 sinθ/cosθ = 4/3

tanθ=4/3

Using the concept of Trigonometry

sinθ=4/5

Putting in equation (2)

AB(4/5)=8 AB=(8×5)/4 AB=40/4 AB=10

Hence, (b) 10, would be the correct option.