If a- - i - 2j - 2k- -b- - 5 and the angle between a- is -6- then the area of the triangle formed by these two vectors as two sides is

The correct option is C 154 We have, #160; |a⃗|=√(1^2+2^2+2^2)=3, |b⃗|=5 Thus area of triangle formed by given vectors =12|a⃗×b⃗| = ...

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Byju's Answer

Standard XII

Mathematics

Applications of Cross Product

If a⃗ = i +...

Question

If $\to a = i + 2 j + 2 k, | \to b | = 5$ and the angle between $\to a$ is $\frac{π}{6}$ , then the area of the triangle formed by these two vectors as two sides is

\frac{15}{2}

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15

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\frac{15}{4}

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\frac{15 \sqrt{3}}{2}

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Solution

The correct option is C $\frac{15}{4}$
We have, $| \to a | = \sqrt{1^{2} + 2^{2} + 2^{2}} = 3,$ $| \to b | = 5$
Thus area of triangle formed by given vectors $= \frac{1}{2} | \to a \times \to b |$ $= \frac{1}{2} | \to a | | \to b | sin \frac{π}{6} = \frac{1}{2} \cdot 3 \cdot 5 \cdot \frac{1}{2} = \frac{15}{4}$

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If →a=i+2j+2k,|→b|=5 and the angle between →a is π6, then the area of the triangle formed by these two vectors as two sides is

The correct option is C 154We have, |→a|=√12+22+22=3, |→b|=5Thus area of triangle formed by given vectors =12|→a×→b|=12|→a||→b|sinπ6=12⋅3⋅5⋅12=154

If $\to a = i + 2 j + 2 k, | \to b | = 5$ and the angle between $\to a$ is $\frac{π}{6}$ , then the area of the triangle formed by these two vectors as two sides is