If the vectors a = λi + muj + 4k, b = -2i + 4j - 2k and c = 2i + 3j + k are coplanar and the projection of a on the vector b is √(54) units, then the sum of all possible values of λ + μ is equal to

If the vectors a = λi + muj + 4k, b = -2i + 4j - 2k and c =… — JEE Main 2023 Mathematics PYQ

JEE Main 2023 · 29 Jan · Shift 1

If the vectors

\vec{a} = \lambda\hat{i} + \mu\hat{j} + 4\hat{k}

\vec{b} = -2\hat{i} + 4\hat{j} - 2\hat{k}

and

\vec{c} = 2\hat{i} + 3\hat{j} + \hat{k}

are coplanar and the projection of

\vec{a}

on the vector

\vec{b}

\sqrt{54}

units, then the sum of all possible values of

\lambda + \mu

is equal to

Show answer

Correct option: C

[JEE Main 2023 · 29 Jan · Shift 1]

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