A-3-7k- and B-5-9k- The direction of the vector A-B is

The correct option is A 8 18 #̂1̂6̂0̂;̂Î ̂ ̂ ̂#̂1̂6̂0̂;̂ , 2ĵ #160; 18 , #160;16k̂ #160; 18 [ A=( 3î ĵ +7k̂ #160; ) ...

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Byju's Answer

Standard XII

Mathematics

Unit Vectors

A=3î-ĵ+7k̂ an...

Question

$A = 3^i -^j + 7^k$ and $B = 5^i -^j + 9^k$ . The direction of the vector $A + B$ is

\frac{8}{18}^I

\frac{- 2^j}{18}

\frac{16^k}{18}

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\frac{3}{\sqrt{31}}

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\frac{B}{\sqrt{336}}

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Solution

The correct option is A $\frac{8}{18}^I$ , $\frac{- 2^j}{18}$ , $\frac{16^k}{18}$
$\begin{matrix} A = (3^i -^j + 7^k) a n d B = 5^i -^j + 9^k \Rightarrow A + B = 8^i - 2^j + 16^k m a g n i t u d e o f (A + B) i s \Rightarrow | A + B | = \sqrt{8^{2} + {(2)}^{2} + {(16)}^{2}} \Rightarrow | A + B | = \sqrt{324} = 18 T h e n, d i r e c t i o n c o s i n e o f (A + B) i s \frac{8}{18}^i, \frac{- 2^j}{18}, \frac{16^k}{18} A n s . \end{matrix}$

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A=3^i−^j+7^k and B=5^i−^j+9^k. The direction of the vector A+B is

The correct option is A 818^I ,−2^j18 ,16^k18A=(3^i−^j+7^k)andB=5^i−^j+9^k⇒A+B=8^i−2^j+16^kmagnitudeof(A+B)is⇒|A+B|=√82+(2)2+(16)2⇒|A+B|=√324=18Then,directioncosineof(A+B)is818^i,−2^j18,16^k18Ans.

$A = 3^i -^j + 7^k$ and $B = 5^i -^j + 9^k$ . The direction of the vector $A + B$ is