If ABCD is a quadrilateral such that AB - - - 2- and AD - - - 2 k- and AC - 2 - - 2- - 3- - 2 k- Then area of quadrilateral ABCD in sq- units is

AB = î + 2ĵ, nbsp; AD = ĵ + 2 k̂ nbsp; AC = 2( î + 2ĵ) + 3(ĵ + 2 k̂) = 2 î + 7 ĵ +6 k̂ We know, BD = nbsp;AD nbsp;AB BD = (ĵ + 2 k̂) (î + 2ĵ)= î ĵ ...

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Standard XII

Physics

Unit Vectors

If ABCD is a ...

Question

If $A B C D$ is a quadrilateral such that $- - \to A B =^i + 2^j$ and $- - \to A D =^j + 2^k$ and $- - \to A C = 2 (^i + 2^j) + 3 (^j + 2^k) .$ Then area of quadrilateral $A B C D$ in sq. units is

\frac{5 \sqrt{21}}{2}

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\frac{3 \sqrt{21}}{2}

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\frac{\sqrt{21}}{2}

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\frac{7}{2}

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Solution

The correct option is A $\frac{5 \sqrt{21}}{2}$
$- - \to A B =^i + 2^j,$ $- - \to A D =^j + 2^k$ $- - \to A C = 2 (^i + 2^j) + 3 (^j + 2^k) = 2^i + 7^j + 6^k$
We know,
$- - \to B D = - - \to A D - - - \to A B$
$- - \to B D = (^j + 2^k) - (^i + 2^j) = -^i -^j + 2^k$
Area of quadrilateral $= \frac{1}{2} | - - \to A C \times - - \to B D |$
Area of quadrilateral $= \frac{1}{2} | (2^i + 7^j + 6^k) \times (-^i -^j + 2^k) |$
Area of quadrilateral $= \frac{1}{2} | 20^i - 10^j + 5^k | = \frac{1}{2} \sqrt{400 + 100 + 25} = \frac{5 \sqrt{21}}{2}$ sq. units

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Unit Vectors

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If ABCD is a quadrilateral such that −−→AB=^i+2^j and −−→AD=^j+2^k and −−→AC=2(^i+2^j)+3(^j+2^k). Then area of quadrilateral ABCD in sq. units is

If $A B C D$ is a quadrilateral such that $- - \to A B =^i + 2^j$ and $- - \to A D =^j + 2^k$ and $- - \to A C = 2 (^i + 2^j) + 3 (^j + 2^k) .$ Then area of quadrilateral $A B C D$ in sq. units is