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Let veca=hati+2hatj+3hatk and vecb=hati+...

Let `veca=hati+2hatj+3hatk and vecb=hati+hatj-hatk`.If `vecc` is a vector such that `veca. vecc=11, vecb.(veca xx vecc)=27 and vecb.vecc=-sqrt3 abs(vecb)`, then `abs(veca xx vecc)^2` is equal to _______

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If veca=hati+hatj + hatk and vecb = hati - 2 hatj+hatk then find the vector vecc such that veca.vecc =2 and veca xx vecc=vecb .

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Let veca=hati+2hatj-hatk, vecb=hati-hatj and vecc=hati-hatj-hatk be three given vectors. If vecr is a vector such that vecr xx veca=vecc xx veca and vecr*vecb=0 , then vecr*veca is equal to _______.

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JEE MAINS PREVIOUS YEAR-JEE MAIN 2023-Question
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