If a-i-j-k- b-i-j-k- c- is a vector perpendicular to a- and coplanar with a- and b- then c-

Let $\to a = i + 2 j + k, \to b = i - j + k a n d \to c = i + j - k,$ a vector in the plane $\to a a n d \to b$ whose projection on $\to c i s \frac{1}{\sqrt{3}} i s . . . . . . . .$

Q. If

\to a = i + 2 j + k

\to b = i - j + k

and

\to c = i + j - k

. A vector in the plane of

\to a

and

\to b

whose projection on

\to c

1 / \sqrt{3}

, is

Q. Let

\to a = i + 2 j + k, \to b = i - j + k

and

\to c = i + j - k

, a vector in the plane

\to a

and

\to b

whose projection on

\to c

\frac{1}{\sqrt{3}}

is _____

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If →a=i+j−k,→b=i−j+k,→c is a vector perpendicular to →a and coplanar with →a and →b then →c=

The correct option is B ±1√6(2i−j+k)Let →c=x^i+y^j+z^k→a⊥→c=→a.→c=0⇒x+y−z=0Also →a,→b,→c are co planar⇒∣∣ ∣∣xyz1−1111−1∣∣ ∣∣=0⇒x(0)−y(−2)+z(2)=0⇒⇒2y+2z=0⇒y+z=0⇒y=−zx+y+y=0⇒x+2y=0⇒x=−2y∴^c=±1√6(2i−j+k)

If $\to a = i + j - k, \to b = i - j + k, \to c$ is a vector perpendicular to $\to a$ and coplanar with $\to a$ and $\to b$ then $\to c =$