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

R× nbsp;a=b× nbsp;a nbsp;and r× nbsp;b=a× nbsp;b ⇒ nbsp;r× nbsp;a= (r× nbsp;b) ⇒ nbsp;r×(a+b)=0 r=λ(a+b) nbsp; [∵ angle between them is 0] ...

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Standard XIII

Mathematics

Linear Combination of Vectors

Let a=î+ĵ; b ...

Question

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

^i -^j + 3^k

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3^i -^j +^k

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3^i +^j -^k

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^i -^j -^k

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Solution

The correct option is C $3^i +^j -^k$
$\to r \times \to a = \to b \times \to a$ and $\to r \times \to b = \to a \times \to b$

$\Rightarrow \to r \times \to a = - (\to r \times \to b)$
$\Rightarrow \to r \times (\to a + \to b) = 0$
$\to r = λ (\to a + \to b)$
$[∵ angle between them is 0]$
$\Rightarrow \to r = λ (^i +^j + 2^i -^k)$
$\Rightarrow \to r = λ (3^i +^j -^k)$
If $λ = 1$ , then
$\to r = 3^i +^j -^k$

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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