Let a- b -2-k- Then- vector r satisfying the equations r-a-b-a and r-b-a-b is

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

Q. Let

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

and

\to c = 5^i +^j -^k

be three vectors. The area of the region formed by the set of points whose position vector

\to r

satisfy the equations

\to r . \to a = 5

and

| \to r - \to b | + | \to r - \to c | = 4

is closest to the integer

Q. Let

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

and

\to c =^i -^j -^k

be three given vectors. If

\to r

is a vector such that

\to r \times \to a = \to c \times \to a

and

\to r \cdot \to b = 0

, then

\to r \cdot \to a

is equal to

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Let →a=^i+^j; →b=2^i−^k. Then, vector →r satisfying the equations →r×→a=→b×→a and →r×→b=→a×→b is

The correct option is C 3^i+^j−^k→r×→a=→b×→a and →r×→b=→a×→b ⇒→r×→a=−(→r×→b) ⇒→r×(→a+→b)=0 →r=λ(→a+→b) [∵ angle between them is 0] ⇒→r=λ(^i+^j+2^i−^k) ⇒→r=λ(3^i+^j−^k) If λ=1, then →r=3^i+^j−^k

Let $\to a =^i +^j; \to b = 2^i -^k$ . Then, vector $\to r$ satisfying the equations $\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$ is