If A-3-4- B-3- and angle between A and B is 30- Find -A-B-

We know that nbsp; |A×B|=|A||B|sinθ We have nbsp; |A|=√(3^2+4^2)=5 nbsp; and nbsp; |B|=√((√(3))^2+( 1)^2)=2 Thus, nbsp; |A×B|=|A||B|sinθ= 5×2×sin30^∘= ...

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Byju's Answer

Standard XII

Physics

Multiplication with Vectors

If A=3î+4ĵ, B...

Question

If $\to A = 3^i + 4^j$ , $\to B = \sqrt{3}^i -^j$ and angle between $\to A$ and $\to B$ is $30^{\circ}$ . Find $| \to A \times \to B |$

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Solution

The correct option is B $5$
We know that
$| \to A \times \to B | = | \to A | | \to B | sin θ$
We have
$| \to A | = \sqrt{3^{2} + 4^{2}} = 5$ and
$| \to B | = \sqrt{(\sqrt{3})^{2} + (- 1)^{2}} = 2$
Thus,
$| \to A \times \to B | = | \to A | | \to B | sin θ = 5 \times 2 \times sin 30^{\circ} = 5$

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Similar questions

Q. If

\to A = 3^i + 4^j

\to B = \sqrt{3}^i -^j

and angle between

\to A

and

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If →A=3^i+4^j, →B=√3^i−^j and angle between →A and →B is 30∘. Find |→A×→B|

The correct option is B 5We know that |→A×→B|=|→A||→B|sinθ We have |→A|=√32+42=5 and |→B|=√(√3)2+(−1)2=2 Thus, |→A×→B|=|→A||→B|sinθ=5×2×sin30∘=5

If $\to A = 3^i + 4^j$ , $\to B = \sqrt{3}^i -^j$ and angle between $\to A$ and $\to B$ is $30^{\circ}$ . Find $| \to A \times \to B |$

The correct option is B $5$
We know that
$| \to A \times \to B | = | \to A | | \to B | sin θ$
We have
$| \to A | = \sqrt{3^{2} + 4^{2}} = 5$ and
$| \to B | = \sqrt{(\sqrt{3})^{2} + (- 1)^{2}} = 2$
Thus,
$| \to A \times \to B | = | \to A | | \to B | sin θ = 5 \times 2 \times sin 30^{\circ} = 5$