Let a and b are vectors such that - a - b -29 and a -2 -3 -4 k-2 -3 -4 k- - b then a - b -7 -2 -3 k-A- - 4B- - 29 C- -1-29D-

The correct option is A ± 4 a× (2î+3ĵ+4k̂)=(2î+3ĵ+4k̂)×b ⇒ (a+b) is parallel to (2î+3ĵ+4k̂) ⇒a+b=λ (2î+3ĵ+4k̂) ⇒ |a+b|=λ |2î+3ĵ+4k̂| ⇒√(29)=λ (±√(29))⇒λ =± 1 ∴ ...

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Byju's Answer

Standard XII

Physics

Vectors and Its Types

Let a and b a...

Question

Let $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b$ then $(\to a + \to b) . (- 7^i + 2^j + 3^k) =$

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$\pm 4$

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$\pm 29$

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$\pm \frac{1}{\sqrt{29}}$

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Solution

The correct option is B
$\pm 4$

$\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b$

$\Rightarrow (\to a + \to b)$ is parallel to $(2^i + 3^j + 4^k)$

$\Rightarrow \to a + \to b = λ (2^i + 3^j + 4^k)$

$\Rightarrow | \to a + \to b | = λ | 2^i + 3^j + 4^k |$

$\Rightarrow \sqrt{29} = λ (\pm \sqrt{29}) \Rightarrow λ = \pm 1$

$∴ \to a + \to b = \pm (2^i + 3^j + 4^k)$

$\Rightarrow \pm (2^i + 3^j + 4^k) . (- 7^i + 2^j + 3^k) = \pm 4$

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Similar questions

If $\to a$ and $\to b$ are vectors such that $| \to a + \to b | = \sqrt{29}$ and $\to a \times (2^i + 3^j + 4^k) = (2^i + 3^j + 4^k) \times \to b,$ then a possible value of $(\to a + \to b) . (- 7^i + 2^j + 3^k)$ is