Find a unit vector perpendicular to both a- and b- where a- - i -2 j -3 k and b- - i -2 j - k

Given that a⃗ =î 2ĵ+3k̂, b⃗=î+2ĵ k̂ Vector perpendicular to both a⃗ and b⃗ is given by #160; ⇒c⃗=a⃗×b⃗ ⇒c⃗=(î 2ĵ+3k̂)× (î+2ĵ k̂) ...

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Definition of Vector

Find a unit v...

Question

Find a unit vector perpendicular to both $\to a$ and $\to b$ , where $\to a = ˆ i - 2 ˆ j + 3 ˆ k$ and $\to b = ˆ i + 2 ˆ j - ˆ k$

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Solution

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\to a = ˆ i + 5 ˆ j + α ˆ k, \to b = ˆ i + 3 ˆ j + β ˆ k

\to c = - ˆ i + 2 ˆ j - 3 ˆ k

| \to b \times \to c | = 5 \sqrt{3}

\to a

\to b

| \to a |^{2}

2 ¯ ¯ ¯ a - 4 ˆ i - 2 ˆ j + ˆ k = 0

¯ ¯ ¯ a

\to a + \to b

\to a - \to b

\to a = \land i + \land j + \land k, \to b = \land i + 2 \land j + 3 \land k

2 \to a + \to b

\to a - 2 \to b

\to a = ˆ i + 2 ˆ j - ˆ k, \to b = ˆ i + ˆ j + ˆ k

(ˆ i + ˆ j)

(ˆ i + ˆ k)

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