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Vector Component

If A⃗ =î +4...

Question

If $\to A =^i + 4^j +^k$ and $\to B = 3^i - 5^j +^k$ , find the unit vector along any vector parallel to the resultant of $\to A$ and $\to B$ .

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Solution

Given,

$\to A =^i + 4^j +^k$ And $\to B = 3^i - 5^j +^k$

Resultant vector, $\to R = \to A + \to B = (^i + 4^j +^k) + (3^i - 5^j +^k) = 4^i -^j + 2^k$

Unit vector of resultant, $^R = \frac{\to R}{∣ ∣ \to R ∣ ∣} = \frac{4^i -^j + 2^k}{\sqrt{4^{2} + 1^{2} + 2^{2}}} = \frac{4^i -^j + 2^k}{\sqrt{21}}$

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Similar questions

\to a - \to b

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

\to b = 3^i + 2^j +^k

\to a = 4^i + 5^j -^k, \to b =^i - 4^j + 5^k, and \to c = 3^i -^j -^k

\to d

\to c

\to b

\to d

\to a = 21

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

\to c =^i - 2^j +^k

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

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

\to c = -^i + 2^j -^k

\to a + \to b

\to b + \to c

If $\to a = 4^i -^j +^k$ and $\to b = 2^i - 2^j +^k,$ then find a unit vector parallel to the vector $\to a + \to b$ .

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