A unit vector parallel to the resultant of the vectors A -4 -2 k- and B -3 -5 -k- isA- 4 -k-B- -4 -k-C- 4 -18-18-k-18D- -4 -18-18-k-18

The correct option is C 4 î√(18) ĵ√(18) k̂√(18)Resultant, R = A + B R = (î + 4ĵ 2 k̂) + (3î + 5ĵ k̂) R = 4î ĵ k̂ Unit vector along R̂ = R|R| R̂ = 4î ...

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Byju's Answer

Standard XII

Physics

Addition and Subtraction in Unit Vector Notation

A unit vector...

Question

A unit vector parallel to the resultant of the vectors $\to A =^i + 4^j - 2^k$ and $\to B = 3^i - 5^j +^k$ is

4^i -^j -^k

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\frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}

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- \frac{4^i}{\sqrt{18}} + \frac{^j}{\sqrt{18}} + \frac{^k}{\sqrt{18}}

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- 4^i +^j +^k

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Solution

The correct option is B $\frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}$
Resultant, $\to R = \to A + \to B$
$\to R = (^i + 4^j - 2^k) + (3^i + 5^j -^k)$
$\to R = 4^i -^j -^k$
Unit vector along $^R = \frac{\to R}{| \to R |}$
$^R = \frac{4^i -^j -^k}{\sqrt{4^{2} + (- 1)^{2} + (- 1)^{2}}}$
$^R = \frac{4^i}{\sqrt{18}} - \frac{^j}{\sqrt{18}} - \frac{^k}{\sqrt{18}}$

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A unit vector parallel to the resultant of the vectors →A=^i+4^j−2^k and →B=3^i−5^j+^k is

The correct option is B 4^i√18−^j√18−^k√18Resultant, →R=→A+→B →R=(^i+4^j−2^k)+(3^i+5^j−^k) →R=4^i−^j−^k Unit vector along ^R=→R|→R| ^R=4^i−^j−^k√42+(−1)2+(−1)2 ^R=4^i√18−^j√18−^k√18

A unit vector parallel to the resultant of the vectors $\to A =^i + 4^j - 2^k$ and $\to B = 3^i - 5^j +^k$ is