Let a- - i - j and b- - 2 i - k- then the point of intersection of lines r-a- - b-a- and r-b- - a-b- is

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. Find a vector perpendicular to each of the vectors

\to a + \to b

and

\to a - \to b

, where

\to a = \land i + \land j + \land k, \to b = \land i + 2 \land j + 3 \land k

Q. 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 =

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Let →a=ˆi+ˆj and →b=2ˆi−ˆk, then the point of intersection of lines →r×→a=→b×→a and →r×→b=→a×→b is

The correct option is C 3ˆi+ˆj−ˆk→r×→a=→b×→a⇒→r=→b+λ→aand →r×→b=→a×→b⇒→r=→a+μ→bFor intersection of both the lines, →b+λ→a=→a+μ→bComparing coefficients, λ=μ=1Hence point of intersection is →r=→a+→b=3^i+^j−^k

Let $\to a = ˆ i + ˆ j$ and $\to b = 2 ˆ i - ˆ k$ , then the point of intersection of lines $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$ is