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Vector Algebra: JEE Mains 2022 June 29 Shift 1

Easy· Cross product· +4 / −1

Let

\vec a=\alpha\hat i+3\hat j-\hat k

,

\vec b=3\hat i-\beta\hat j+4\hat k

and

\vec c=\hat i+2\hat j-2\hat k

where

\alpha,\beta\in\mathbb R

, be three vectors. If the projection of

\vec a

on

\vec c

is

\dfrac{10}{3}

and

\vec b\times\vec c=-6\hat i+10\hat j+7\hat k

, then the value of

\alpha+\beta

is equal to :

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