JEE Main 2020MathematicsVector AlgebraHardMCQ

JEE Main 2020 — Vector Algebra Question with Solution

JEE Main 2020 (04 Sep Shift 1)

Question

Let x0 be the point of local maxima of  fx=a→·b→×c→, wherea→=xi^-2j^+3k^,  b→=-2i^+xj^-k^ and c→=7i^-2j^+xk^. Then the value of a→·b→+b→·c→+c→·a→ at x=x0 is:

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Show full solutionCorrect option: D
Correct answer
D-22

Step-by-step explanation

fx=a→  b→  c→=x      −2      3−2      x     −17       −2      x

=xx2−2+2−2x+7+34−7x

=x3−2x−4x+14+12−21x

fx=x3−27x+26

f'x=3x2−27=3x−3x+3

           

so local maxima point is x0=-3

Now a→.b→+b→.c→+c→.a→=−2x−2x−3-14−2x−x+7x+4+3x=3x−13

at x=x0=−3

a→.b→+b→.c→+c→.a→=−9−13=−22

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About this question

This is a previous-year question from JEE Main 2020, covering the Vector Algebra chapter of Mathematics. PrepSharp catalogues every PYQ from JEE Main with a verified answer key and step-by-step solution prepared by IIT alumni — so you can search by chapter, topic or year and revise efficiently.