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If a⃗=i+2j+2k...

Question

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

A

$\frac{15}{2}$

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B

$15$

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C

$\frac{15}{4}$

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D

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

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Solution

The correct option is C
$\frac{15}{4}$

$a r e a = \frac{1}{2} | a \times b | = \frac{1}{2} | a | | b | s i n \frac{π}{6} = \frac{15}{4}$

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