Find the unit vector in the direction of the resultant of vectors -2 -3 k-2 -k- and 3 -A- 1-2-1-2-4-5 -2k-B- 3-5 -2-1-2-4-5 -2k-C- 3-5 -10-1-5 -10-4-5 -10k-D- 3-5 -2-1-2-4-5 -2k-

The correct option is B 35 √(2)î + 1√(2)ĵ + 45 √(2)k̂Let a be the resultant of given vectors. Then a = (î + 2 ĵ + 3 k̂) + ( î + 2ĵ + k̂) + (3 î + ĵ) = 3 î + 5 ...

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Byju's Answer

Standard XII

Physics

Unit Vectors

Find the unit...

Question

Find the unit vector in the direction of the resultant of vectors $^i + 2^j + 3^k, -^i + 2^j +^k$ and $3^i +^j$ .

\frac{1}{\sqrt{2}}^i + \frac{1}{\sqrt{2}}^j + \frac{4}{5 \sqrt{2}}^k

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\frac{3}{5 \sqrt{2}}^i + \frac{1}{\sqrt{2}}^j + \frac{4}{5 \sqrt{2}}^k

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\frac{3}{5 \sqrt{10}}^i + \frac{1}{5 \sqrt{10}}^j + \frac{4}{5 \sqrt{10}}^k

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\frac{3}{5 \sqrt{2}}^i - \frac{1}{\sqrt{2}}^j + \frac{4}{5 \sqrt{2}}^k

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Solution

The correct option is B $\frac{3}{5 \sqrt{2}}^i + \frac{1}{\sqrt{2}}^j + \frac{4}{5 \sqrt{2}}^k$
Let $\to a$ be the resultant of given vectors.
Then $\to a = (^i + 2^j + 3^k) + (-^i + 2^j +^k) + (3^i +^j)$
$= 3^i + 5^j + 4^k$
$| \to a | = \sqrt{(3)^{2} + (5)^{2} + (4)^{2}}$
$= \sqrt{9 + 25 + 16} = \sqrt{50} = 5 \sqrt{2}$
Now unit vector along $\to a = \frac{\to a}{| \to a |} = \frac{3}{5 \sqrt{2}}^i + \frac{1}{\sqrt{2}}^j + \frac{4}{5 \sqrt{2}}^k$

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Find the unit vector in the direction of the resultant of vectors ^i+2^j+3^k,−^i+2^j+^k and 3^i+^j.

The correct option is B 35√2^i+1√2^j+45√2^kLet →a be the resultant of given vectors. Then →a=(^i+2^j+3^k)+(−^i+2^j+^k)+(3^i+^j) =3^i+5^j+4^k |→a|=√(3)2+(5)2+(4)2 =√9+25+16=√50=5√2 Now unit vector along →a=→a|→a|=35√2^i+1√2^j+45√2^k

Find the unit vector in the direction of the resultant of vectors $^i + 2^j + 3^k, -^i + 2^j +^k$ and $3^i +^j$ .