The unit vector in the direction of the sum of the vectors- a -2 -2 -5 k- and b -2 -3 k-

A=2î+2ĵ 5k̂ and nbsp;b=2î+ĵ+3k̂ The sum of the given vector is, c=a+b =4î+3ĵ 2k̂ |c|=√(4^2+3^2+( 2)^2)=√(29) Thus, the required unit vector is, ĉ=c|c|=4√(29 ...

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Standard XII

Mathematics

Addition of Vectors

The unit vect...

Question

The unit vector in the direction of the sum of the vectors, $\to a = 2^i + 2^j - 5^k$ and $\to b = 2^i +^j + 3^k$ is _____

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Solution

$\to a = 2^i + 2^j - 5^k$ and $\to b = 2^i +^j + 3^k$
The sum of the given vector is,
$\to c = \to a + \to b$
$= 4^i + 3^j - 2^k$

$| \to c | = \sqrt{4^{2} + 3^{2} + (- 2)^{2}} = \sqrt{29}$

Thus, the required unit vector is,
$^c = \frac{\to c}{| \to c |} = \frac{4}{\sqrt{29}}^i + \frac{3}{\sqrt{29}}^j - \frac{2}{\sqrt{29}}^k$

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The unit vector in the direction of the sum of the vectors, →a=2^i+2^j−5^k and →b=2^i+^j+3^k is _____

→a=2^i+2^j−5^k and →b=2^i+^j+3^k The sum of the given vector is, →c=→a+→b =4^i+3^j−2^k |→c|=√42+32+(−2)2=√29 Thus, the required unit vector is, ^c=→c|→c|=4√29^i+3√29^j−2√29^k

The unit vector in the direction of the sum of the vectors, $\to a = 2^i + 2^j - 5^k$ and $\to b = 2^i +^j + 3^k$ is _____