JEE Main 2019MathematicsVector AlgebraEasyMCQ

JEE Main 2019 — Vector Algebra Question with Solution

JEE Main 2019 (09 Apr Shift 2)

Question

If a unit vector a→ makes angles π3 with i^, π4 with j^ and θ∈0,π with k^, then a value of θ is:

Choose an option

Show full solutionCorrect option: D
Correct answer
D2π3

Step-by-step explanation

The unit vector a→ makes angle π3, π4 and θ with i^, j^ & k^ respectively.

Hence, the direction cosines of the vector a→ are cosα=cosπ3=12, cosβ=cosπ4=12 and cosγ=cosθ

For a line having direction cosines as cosα, cosβ, cosγ

⇒cos2α+cos2β+cos2γ=1

⇒14+12+cos2θ=1

⇒cos2θ=1-34=14

⇒cos2θ=±12

⇒θ=π3 or 2π3.

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About this question

This is a previous-year question from JEE Main 2019, 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.