If a - 2- - 3- - 6k- b - 3- - 6- - 2k- c - 6- - 2- - 3k- then a-b-

A×b = î amp; ĵ amp; k̂ 2 amp; 3 amp; 6 3 amp; 6 amp; 2 = 42î + 14ĵ 21k̂ = 7 (6î + 2ĵ 3k̂) =7c ...

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Byju's Answer

Standard XII

Physics

Subtraction of a Vector

If a = 2î + 3...

Question

If $\to a = 2^i + 3^j + 6^k, \to b = 3^i - 6^j + 2^k, \to c = 6^i + 2^j - 3^k,$ then $\to a \times \to b =$

7 \to c

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\to c

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5 \to c

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4 \to c

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Solution

The correct option is A $7 \to c$
$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & 3 & 6 3 & - 6 & 2 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 42^i + 14^j - 21^k$
$= 7 (6^i + 2^j - 3^k)$
$= 7 \to c$

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A = 2^i + 3^j + 6^k

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a = 2^i - 6^j - 3^k, b = 4^i + 3^j -^k

Let $\to a = \frac{1}{7} (2^i + 3^j + 6^k), \to b = \frac{1}{7} (6^i + 2^j - 3^k), \to c = c_{1}^i + c_{2}^j + c - 3^k$ and matrix $A = ⎡ ⎢ ⎢ ⎢ ⎣ \begin{matrix} \frac{2}{7} & \frac{3}{7} & \frac{6}{7} \frac{6}{7} & \frac{2}{7} & - \frac{3}{7} c_{1} & c_{2} & c_{3} \end{matrix} ⎤ ⎥ ⎥ ⎥ ⎦$
If $A A^{T} = I, t h e n \to c$ is equal to