Ab- are such that -a- -3- -b- -2 and a- b-3- Then the area of the triangle with adjacent sides a-2b and 2a- b is -

The correct option is B 92 Area of triangle with adjacent sides: a⃗ +2b⃗ and 2a⃗ +b⃗ is = 1 2 .| ( a⃗ +2b⃗ #160; ) ×( 2a⃗ +b⃗ #160; ) ...

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Byju's Answer

Standard XII

Physics

Vector Addition

ab, are such ...

Question

$¯ ¯ ¯ a ¯ ¯ b,$ are such that $| ¯ ¯ ¯ a | = \sqrt{3}, | ¯ ¯ b | = 2$ and $(¯ ¯ ¯ a, ¯ ¯ b) = \frac{π}{3}$ . Then the area of the triangle with adjacent sides $¯ ¯ ¯ a + 2 ¯ ¯ b$ and $2 ¯ ¯ ¯ a + ¯ ¯ b$ is :

5 \sqrt{3}

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15

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\frac{9}{2}

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\frac{15}{2}

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Solution

The correct option is B $\frac{9}{2}$
Area of triangle with adjacent sides:
$\to a + 2 \to b a n d 2 \to a + \to b$ is
$= \frac{1}{2} . ∣ ∣ (\to a + 2 \to b) \times (2 \to a + \to b) ∣ ∣$
$= \frac{1}{2} . ∣ ∣ (\to a \times 2 \to a) + (\to a \times \to b) + (2 \to b \times 2 \to a) + (2 \to b \times \to b) ∣ ∣$
$= \frac{1}{2} . ∣ ∣ 0 + (\to a \times \to b) + 4 (\to b \times \to a) + 0 ∣ ∣$
$= \frac{1}{2} . ∣ ∣ 4 (\to b \times \to a) - (\to b \times \to a) ∣ ∣$
$= \frac{1}{2} . ∣ ∣ 3 (\to b \times \to a) ∣ ∣$
$= ∣ ∣ ∣ \frac{- 3}{2} (\to a \times \to b) ∣ ∣ ∣$
( $∵$ Angle between $\to a a n d \to b = \frac{π}{3}$ )
$= ∣ ∣ ∣ \frac{- 3}{2} | a | | b | sin \frac{π}{3} ∣ ∣ ∣$
$= \frac{3}{2} \times \sqrt{3} \times 2 \times \frac{\sqrt{3}}{2} = \frac{9}{2}$

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¯¯¯a¯¯b, are such that |¯¯¯a|=√3,|¯¯b|=2 and (¯¯¯a,¯¯b)=π3. Then the area of the triangle with adjacent sides ¯¯¯a+2¯¯b and 2¯¯¯a+¯¯b is :

$¯ ¯ ¯ a ¯ ¯ b,$ are such that $| ¯ ¯ ¯ a | = \sqrt{3}, | ¯ ¯ b | = 2$ and $(¯ ¯ ¯ a, ¯ ¯ b) = \frac{π}{3}$ . Then the area of the triangle with adjacent sides $¯ ¯ ¯ a + 2 ¯ ¯ b$ and $2 ¯ ¯ ¯ a + ¯ ¯ b$ is :