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Applications of Cross Product

If a⃗=2î-6ĵ...

Question

If $\to a = 2^i - 6^j - 3^k, \to b = 4^i + 3^j -^k$ , then $sin (\to a, \to b) =$

A

\frac{5}{\sqrt{26}}

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B

\frac{5}{26}

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C

5 \sqrt{26}

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D

\sqrt{\frac{5}{26}}

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Solution

The correct option is A $\frac{5}{\sqrt{26}}$
$\to a \times \to b = ∣ ∣ ∣ ∣ ∣ \begin{matrix} ^i & ^j & ^k 2 & - 6 & - 3 4 & 3 & 1 \end{matrix} ∣ ∣ ∣ ∣ ∣ = 15^i + 10^j + 30^k$
$| \to a \times \to b | = | \to a | | \to b | sin θ$
$5 \times 7 = 7 \times \sqrt{26} sin θ$
$sin θ = \frac{5}{\sqrt{26}}$

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Similar questions

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

\to c = 4^i + 3^k

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

\to a = 3^i - 2^j +^k,

\to b = 2^i - 4^j - 3^k, \to c = -^i + 2^j + 2^k

\to a + \to b + \to c = 4^i - 4^j

\to a =^i -^j + 2^k, \to b = 2^i + 3^j +^k, \to c =^i -^k

, then magnitude of

\to a + 2 \to b - 3 \to c

\sqrt{78}

| \to a | = \sqrt{26}, ∣ ∣ \to b ∣ ∣ = 7

∣ ∣ \to a \times \to b ∣ ∣ = 35

\to a . \to b

\to a = 2^i - 3^j +^k

\to b = 3^i + 2^j

\to a \times \to b

If $\to r \times \to b = \to c \times \to b$ and $\to r . \to a = 0$ where $\to a = 2^i + 3^j -^k, \to b = 3^i -^j +^k$ and $\to c =^i +^j + 3^k$ , then $\to r$ is equal to

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