If A- - 4 - - 3 - and B- - 6 - - 8 - then magnitude and direction of A- - B- will be

The correct option is B 5 √(5), tan^ 1 (12) If #160; A=4î 3ĵ B=6î+8ĵ A+B=4î 3ĵ+6î+8ĵ #160; #160; #160; #160; #160; #160; ...

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Byju's Answer

Standard XII

Mathematics

Derivative from First Principle

If A⃗ = 4 î...

Question

If $\to A = 4^i - 3^j$ and $\to B = 6^i + 8^j$ then magnitude and direction of $\to A + \to B$ will be

5, t a n^{- 1} (\frac{3}{4})

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5 \sqrt{5}, t a n^{- 1} (\frac{1}{2})

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5, t a n^{- 1} (\frac{1}{2})

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25, t a n^{- 1} (\frac{3}{4})

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Solution

The correct option is B $5 \sqrt{5}, t a n^{- 1} (\frac{1}{2})$
If
$\to A = 4^i - 3^j \to B = 6^i + 8^j$
$\to A + \to B = 4^i - 3^j + 6^i + 8^j$
$= 10^i + 5^j$

Magnitude $= \sqrt{10^{2} + 5^{2}} = \sqrt{100 + 25} = \sqrt{125} = 5 \sqrt{5}$

$ϕ = t a n^{- 1} \frac{5}{10} = t a n^{- 1} \frac{1}{2}$

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If →A=4^i−3^j and →B=6^i+8^j then magnitude and direction of →A+→B will be

The correct option is B 5√5,tan−1(12)If →A=4^i−3^j→B=6^i+8^j→A+→B=4^i−3^j+6^i+8^j =10^i+5^jMagnitude =√102+52=√100+25=√125=5√5ϕ=tan−1510=tan−112

If $\to A = 4^i - 3^j$ and $\to B = 6^i + 8^j$ then magnitude and direction of $\to A + \to B$ will be

The correct option is B $5 \sqrt{5}, t a n^{- 1} (\frac{1}{2})$
If
$\to A = 4^i - 3^j \to B = 6^i + 8^j$
$\to A + \to B = 4^i - 3^j + 6^i + 8^j$
$= 10^i + 5^j$

Magnitude $= \sqrt{10^{2} + 5^{2}} = \sqrt{100 + 25} = \sqrt{125} = 5 \sqrt{5}$

$ϕ = t a n^{- 1} \frac{5}{10} = t a n^{- 1} \frac{1}{2}$