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If |A⃗×B⃗|=√3 A⃗·B⃗, then the value of |A⃗+B⃗| is

Asked in NEET 2004 · Magnitude of the resultant

Answer: (1) (A²+B²+AB)^1/2

Step-by-step solution

Given: |A⃗×B⃗|=√3(A⃗·B⃗).

Idea: first extract the angle from the condition, then feed it into the parallelogram law.

AB sin θ=√3 AB cos θ, so tan θ=√3 and θ=60°.

cos 60°=1/2.

|A⃗+B⃗|=√A²+B²+2AB cos θ=√A²+B²+2AB(1/2).

=(A²+B²+AB)^1/2.

Why the other options are wrong

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