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← JEE Main 2014 · 9 Apr · Shift 1
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JEE Main 2014 · 9 Apr · Shift 1, Mathematics question 85

If ∣a⃗∣=2|\vec a|=2, ∣b⃗∣=3|\vec b|=3 and ∣2a⃗−b⃗∣=5|2\vec a-\vec b|=5, then ∣2a⃗+b⃗∣|2\vec a+\vec b| equals :

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Answer and worked solution

Official answer: C

∣2a⃗−b⃗∣2=16+9−4a⃗⋅b⃗=25|2\vec a-\vec b|^2=16+9-4\vec a\cdot\vec b=25, so a⃗⋅b⃗=0\vec a\cdot\vec b=0. Then ∣2a⃗+b⃗∣2=25|2\vec a+\vec b|^2=25, and ∣2a⃗+b⃗∣=5|2\vec a+\vec b|=5.

Topics:Dot product
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