Let a-a1-a2-a3k-b-b1-b2-b3k-c-c1-c2-c3k-If -c-1 and a-b-c-0 then -a1 a2 a3 b1 b2 b3 c1 c2 c3-2-

The correct option is D |a×b|^2 (a×b)×c=0 ⇒c is parallel to a×b Given |c|=1 ⇒c=a×b|a×b| ∴a×b.c=|a×b|^2|a×b| Hence nbsp; |a ...

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Multiplication with Vectors

Let a=a1î+a...

Question

Let $\to a = a_{1}^i + a_{2}^j + a_{3}^k, \to b = b_{1}^i + b_{2}^j + b_{3}^k, \to c = c_{1}^i + c_{2}^j + c_{3}^k$ .If $∣ ∣ \to c ∣ ∣ = 1$ and $(\to a \times \to b) \times \to c = 0$ then
${∣ ∣ ∣ ∣ \begin{matrix} a_{1} & a_{2} & a_{3} b_{1} & b_{2} & b_{3} c_{1} & c_{2} & c_{3} \end{matrix} ∣ ∣ ∣ ∣}^{2} =$

0

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1

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{∣ ∣ \to a ∣ ∣}^{2} {∣ ∣ ∣ \to b ∣ ∣ ∣}^{2}

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{∣ ∣ ∣ \to a \times \to b ∣ ∣ ∣}^{2}

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Solution

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Similar questions

\to a, \to b, \to c

a_{1}^i + a_{2}^j + a_{3}^k, b_{1}^i + b_{2}^j + b_{3}^k, c_{1}^i + c_{2}^j + c_{3}^k

\to a \times (\to b + \to c) = \to a \times \to b + \to a \times \to c

\to a = a_{1}^i + a_{2}^j + a_{3}^k; \to b = b_{1}^i + b_{2}^j + b_{3}^k;

\to c = c_{1}^i + c_{2}^j + c_{3}^k

[3 \to a + \to b, 3 \to b + \to c, 3 \to c + \to a]

= λ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \to a \cdot^i & \to a \cdot^j & \to a \cdot^k \to b \cdot^i & \to b \cdot^j & \to b \cdot^k \to c \cdot^i & \to c \cdot^j & \to c \cdot^k \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

\frac{λ}{4}

\to a = a_{1}^i + a_{2}^j + a_{3}^k; \to b = b_{1}^i + b_{2}^j + b_{3}^k;

\to c = c_{1}^i + c_{2}^j + c_{3}^k

[3 \to a + \to b, 3 \to b + \to c, 3 \to c + \to a]

= λ ∣ ∣ ∣ ∣ ∣ ∣ \begin{matrix} \to a \cdot^i & \to a \cdot^j & \to a \cdot^k \to b \cdot^i & \to b \cdot^j & \to b \cdot^k \to c \cdot^i & \to c \cdot^j & \to c \cdot^k \end{matrix} ∣ ∣ ∣ ∣ ∣ ∣

\frac{λ}{4}

a_{1}^i + a_{2}^j + a_{3}^k

b_{1}^i + b_{2}^j + b_{3}^k

\to a = a_{1}^i + a_{2}^j - a_{3}^k

\to b = b_{1}^i + b_{2}^j - b_{3}^k

\to a \times \to b

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