Test Index

UPSC NDA II 2014 Mathematics Paper

Show Para Hide Para

For the next four (04) items that follow:

\vec{a}+\vec{b}+\vec{c}=\vec{0}

and

|\vec{a}|=3,|\vec{b}|=5

and

|\vec{c}|=7

[NDA II 2014]

© examsnet.com

Question : 97 of 120

Marks: +1, -0

What is the angle between

\vec{a}

\vec{b}

π/6
π/4
π/3
π/2

Solution:

\vec{a}+\vec{b}=-\vec{c}

\Rightarrow (\vec{a}+\vec{b})\cdot (\vec{a}+\vec{b})=-\vec{c}\cdot -\vec{c}

\Rightarrow \vec{a}\cdot \vec{a}+\vec{b}\cdot \vec{b}+\vec{2a}\cdot \vec{b}=\vec{c}\cdot \vec{c}

\Rightarrow 2|\vec{a}||\vec{b}|\cos\theta=49-25-9=15

\Rightarrow 2\times 3\times 5\cos\theta=15

\Rightarrow \cos\theta=\frac{1}{2}

\Rightarrow \theta=\frac{\pi}{3}

© examsnet.com

Go to Question:

Prev Question

Next Question