Let vec(a)=2hati-hatj+hatk, vec(b)=hati+2hatj-hatk and vec(c)=hati+hatj-2hatk be three vectors. A vector in the plane of vec(b) and vec(c) whose projection on vec(a) is of magnitude sqrt((2)/(3)), is

Let vec(a)=2hati-hatj+hatk, vec(b)=hati+2hatj-hatk and vec(c)=hati+hat

1.	Let vec(a)=2hati-hatj+hatk, vec(b)=hati+2hatj-hatk and vec(c)=hati+hatj-2hatk be three vectors. A vector in the plane of vec(b) and vec(c) whose projection on vec(a) is of magnitude sqrt((2)/(3)), is
Answer» `2hati+3hatj-3hatk` `2hati+3hatj+3hatk` `2hati-5hatj+5hatk` `2hati+hatj+5hatk` SOLUTION :Any vectors in the PLANE of `vec(B) and vec(c)" is" vec(r)=mvec(b)+vec(c)` `=(m+1)HATI+(2m+1)hatj+(-m-2)hatk` Projection of `vec(r)" on "vec(c)=(vec(r).vec(a))/(\|vec(a)\|)=\|sqrt((2)/(3))\|` `Rightarrow -m-1=pm 2` `Rightarrow m=-3 and 1` `"Hence ", vec(r)=-2hati-5hatj+hatk and vec(r)=2hati+3hatj-3hatk`

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Let vec(a)=2hati-hatj+hatk, vec(b)=hati+2hatj-hatk and vec(c)=hati+hatj-2hatk be three vectors. A vector in the plane of vec(b) and vec(c) whose projection on vec(a) is of magnitude sqrt((2)/(3)), is

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