12. If | AXB| = √3 A.B ,then the value of A+B | is (a) (A? +B? + AB )1/2 (b) ( A² + B + AB /V3) 1/2 (c) (A + B) (d) ( A²+B? + V3 AB) 1/2
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Answer:
We know that,
A×B=ABsinθ
Also, A.B=ABcosθ
Given : ∣A×B∣=
3
A.B
Using ∣A×B∣=∣A∣∣B∣sinθ
We get ∣A×B∣=ABsinθ
A.B=∣A∣∣B∣cosθ
∴ ABsinθ=
3
ABcosθ
tanθ=
3
⟹θ=60
o
Now (A+B)
2
=A
2
+B
2
+2A.B
=A
2
+B
2
+2ABcosθ
=A
2
+B
2
+2AB×
2
1
=A
2
+B
2
+AB
or ∣A+B∣=(A
2
+B
2
+AB)
1/2
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