JEE Main2012MathematicsVector AlgebraActual

If u = j +4 k , v = i +3 k and w = i + j are vectors in 3-dimensional space, then the maximum possible value of | u v w | is

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Correct answer

B. 5

Step-by-step solution

Let u = j +4 k , v = i -3 k and w = i + j Now, u v = | array ccc i & j & k 0 & 1 & 4 1 & 0 & -3 array | = i (-3+ j -4(+ k )-1 ( ) =-3 i +4 j - k Now, aligned & ( u v ) w =(-3 i +4 j - k ) ( i + j ) & =-3 +4 aligned Now, maximum possible value of |-3 +4 |= (-3)^2+(4)^2 = 25 =5

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