If a- -2- -3k- and b-3- - -k- and r- a-b- a-r- b-a- b- then a unit vector in the direction of r is

The correct option is B ± 1 3 ( 2î ĵ +2k̂) We have r× b=a× b #160;and r× a=b× a ⇒ r× b= r× a ⇒ r× b+r× a=0 ⇒ r× (b+a)=0 ...

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Byju's Answer

Standard XII

Mathematics

Addition of Vectors

If a=î -2ĵ ...

Question

If $a =^i - 2^j + 3^k$ and $b = - 3^i +^j -^k$ and $r \times a = b \times a, r \times b = a \times b$ , then a unit vector in the direction of $r$ is

\pm \frac{1}{3} (- 2^i +^j -^k)

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\pm \frac{1}{3} (- 2^i -^j + 2^k)

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\pm \frac{1}{3} (- 2^i -^j - 2^k)

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None of htese

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Solution

The correct option is B $\pm \frac{1}{3} (- 2^i -^j + 2^k)$
We have
$r \times b = a \times b$
and
$r \times a = b \times a$
$\Rightarrow r \times b = - r \times a$
$\Rightarrow r \times b + r \times a = 0$
$\Rightarrow r \times (b + a) = 0$
$\Rightarrow r ∥ b + a$
$\Rightarrow r = λ (b + a)$
$\Rightarrow r = \pm \frac{b + a}{| a + b |} = \pm \frac{1}{3} (- 2^i -^j + 2^k)$

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If a=^i−2^j+3^k and b=−3^i+^j−^k and r×a=b×a,r×b=a×b, then a unit vector in the direction of r is

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