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Question:

Let ⃗a=^i+^j+^k, ⃗c=^j−^k and a vector ⃗b be such that ⃗a×⃗b=⃗c and ⃗a⋅⃗b=3. Then |⃗b| equals?

√113

11√3

113

√113

Solution:

Given→a=^i+^j+^k,→c=^j−^k|→a|=√1+1+1=√3|→c|=√1+1=√2→a×→b=→c⟹|→a|∣∣→b∣∣sinθ=|→c|⟹|→a|∣∣→b∣∣sinθ=√2...[1]→a.→b=3⟹|→a|∣∣→b∣∣cosθ=3...[2]Dividing [1] by [2], we gettanθ=√23⟹sinθ=√2√11Substituting value ofsinθin [1] ,we get⟹|→a|∣∣→b∣∣sinθ=√2⟹√3∣∣→b∣∣√2√11=√2∣∣→b∣∣=√11√3Hence, answer is option (A).