If -a- - -26- -b- - 7 and -a - b- - 35- find a-b- - Maths Q - A

Step 1: Solve for value of cos(θ).Given, |a|=√(26), |b|=7, |a×b|=35We know that,|a×b|=|a||b|sin(θ)0ex0ex⇒ 35= (√(26))(7)sin(θ)0ex0ex⇒sin(θ)=5/√(26)Using the ...

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Byju's Answer

Standard XII

Mathematics

Derivative from First Principle

If |a| = √26,...

Question

If $|\vec{a}| = \sqrt{26}, |\vec{b}| = 7$ and $|\vec{a} \times \vec{b}| = 35$ , find $\vec{a} \cdot \vec{b}$

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Solution

Step 1: Solve for value of $\cos (θ) .$
Given,
$|\vec{a}| = \sqrt{26}, |\vec{b}| = 7, |\vec{a} \times \vec{b}| = 35$
We know that,
$|\vec{a} \times \vec{b}| = |\vec{a}| |\vec{b}| \sin (θ) \Rightarrow 35 = (\sqrt{26}) (7) \sin (θ) \Rightarrow \sin (θ) = \frac{5}{\sqrt{26}}$
Using the identity, $\sin^{2} (A) + \cos^{2} (A) = 1$
$\cos (θ) = \sqrt{1 - \sin^{2} (θ)} = \sqrt{[1 - {(\frac{5}{\sqrt{26}})}^{2}]}$
$= \sqrt{[\frac{(26 - 25)}{26}]} = \frac{1}{\sqrt{26}}$
Step 2: Solve for $\vec{a} \cdot \vec{b} .$
$\vec{a} \cdot \vec{b} = |\vec{a}| |\vec{b}| \cos (θ)$
$= (\sqrt{26}) (7) (\frac{1}{\sqrt{26}}) = 7$
Hence, the value of $\vec{a} \cdot \vec{b}$ is $7$

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If a→=26,b→=7and a→×b→=35, find a→·b→

If $|\vec{a}| = \sqrt{26}, |\vec{b}| = 7$ and $|\vec{a} \times \vec{b}| = 35$ , find $\vec{a} \cdot \vec{b}$