The angle between a and b is - -6 - then angle between 2 a and 3 b is

The correct option is D π /6 the angle will be same only the magnitude will change #160;the angle say θ=π6 a⃗·b⃗= | a⃗ | | b⃗ |cosπ6 a⃗·b ...

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Standard XII

Mathematics

Applications of Dot Product

The angle bet...

Question

The angle between $a$ and $b$ is $π / 6$ , then angle between 2 $a$ and 3 $b$ is

π / 3

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π / 2

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π / 6

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none of these

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Solution

The correct option is D $π / 6$
the angle will be same only the magnitude will change
the angle say $θ = \frac{π}{6}$
$\to a \cdot \to b = | \to a | ∣ ∣ \to b ∣ ∣ cos \frac{π}{6}$
$\to a \cdot \to b = \frac{\sqrt{3}}{2} | \to a | ∣ ∣ \to b ∣ ∣$
$\to 2 a \cdot \to 3 b = | 2 \to a | ∣ ∣ 3 \to b ∣ ∣ cos α$
$6 \to a \cdot \to b = 2 | \to a | 3 ∣ ∣ \to b ∣ ∣ cos α$
$\to a \cdot \to b = | \to a | ∣ ∣ \to b ∣ ∣ cos α$
$| \to a | ∣ ∣ \to b ∣ ∣ cos \frac{π}{6} = | \to a | ∣ ∣ \to b ∣ ∣ cos α$
$α = \frac{π}{6}$

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The angle between a and b is π/6 , then angle between 2a and 3b is

The angle between $a$ and $b$ is $π / 6$ , then angle between 2 $a$ and 3 $b$ is