For non-zero vectors →a,→b,→c; |(→a×→b).→c|=|→a||→b||→c| holds if
A
→a.→b=0,→b.→c=0
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B
→b.→c=0,→c.→a=0
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C
→c.→a=0,→a.→b=0
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D
→a.→b=→b.→c=→c.→a=0
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Solution
The correct option is D→a.→b=→b.→c=→c.→a=0 We have
∣∣(→a×→b).→c∣∣=|→c|∣∣→a×→b∣∣cosϕ =|→c||→a|∣∣→b∣∣sinθcosϕ (where ϕ is angle between →a+→b & →c θ is angle between →a & →b) sinθ=1ωϕ=1 θ=π2ϕ=0 So →a⊥→b→c||→a×→b So →a.→b=→c.→a=→c.→b=0