Let a-3- -2-2k- and b- -2-2k- be two vectors- If a vector perpendicular to both the vectors a-b and a-b has the magnitude 12 then one such vector is -

A=3î +2ĵ+2k̂ b=î +2ĵ 2k̂ a+b=4î+4ĵ a b=2î+4k̂ As nbsp;a vector rperpendicular to both the vectors a+ nbsp; b and nbsp;a nbsp; b has the magnitude 12 r= ...

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Byju's Answer

Standard XIII

Mathematics

Cross Product of Two Vectors

Let a=3î +2ĵ+...

Question

Let $\to a = 3^i + 2^j + 2^k$ and $\to b =^i + 2^j - 2^k$ be two vectors. If a vector perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$ then one such vector is :

4 (2^i + 2^j +^k)

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4 (2^i + 2^j -^k)

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4 (2^i - 2^j -^k)

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4 (- 2^i - 2^j +^k)

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Solution

The correct option is C $4 (2^i - 2^j -^k)$
$\to a = 3^i + 2^j + 2^k$
$\to b =^i + 2^j - 2^k$
$\to a + \to b = 4^i + 4^j$
$\to a - \to b = 2^i + 4^k$
As a vector $\to r$ perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$
$\to r = 12 \cdot^n$
$^n = \frac{(\to a + \to b) \times (\to a - \to b)}{∣ ∣ ∣ (\to a + \to b) \times (\to a - \to b) ∣ ∣ ∣}$

$^n = \frac{8 [2^i - 2^j -^k]}{8 \cdot \sqrt{4 + 4 + 1}} = \frac{2^i - 2^j -^k}{3}$

$∴ \to r = \frac{12}{3} (2^i - 2^j -^k) = 4 (2^i - 2^j -^k)$

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Let →a=3^i+2^j+2^k and →b=^i+2^j−2^k be two vectors. If a vector perpendicular to both the vectors →a+→b and →a−→b has the magnitude 12 then one such vector is :

Let $\to a = 3^i + 2^j + 2^k$ and $\to b =^i + 2^j - 2^k$ be two vectors. If a vector perpendicular to both the vectors $\to a + \to b$ and $\to a - \to b$ has the magnitude $12$ then one such vector is :