Let U → = i ^ + j ^ , V → = i ^ - j ^ and W → = 3 i ^ + 5 j ^ + 3 k ^ . If n ^ is a unit vector such that U → ⋅ n ^ = 0 and V → ⋅ n ^ = 0 , then W → ⋅ n ^ is equal to

Question

Let U → = i ^ + j ^ , V → = i ^ - j ^ and W → = 3 i ^ + 5 j ^ + 3 k ^ . If n ^ is a unit vector such that U → ⋅ n ^ = 0 and V → ⋅ n ^ = 0 , then W → ⋅ n ^ is equal to,

MARKS App · Accepted Answer

∵ n ^ is perpendicular to both U → and V → Hence, n ^ = λ U → × V → n ^ = ± λ - 2 k ^ Since n ^ is unit vector hence n ^ = 1 ⇒ 2 λ = 1 ⇒ λ = 1 2 Hence, n ^ = ± k ^ So, W → ⋅ n ^ = 3

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