Test Index

UPSC NDA 2 2016 Mathematics Solved Paper

Show Para Hide Para

Consider the following for the next two (02) items that follow:

Let

\overset{\rightarrow}{a},\overset{\rightarrow}{b}

and

\overset{\rightarrow}{c}

be three vectors such that

\overset{\rightarrow}{a}++\overset{\rightarrow}{b}+\overset{\rightarrow}{c}=0

and

\left|\overset{\rightarrow}{a}\right|=10,\left|\overset{\rightarrow}{b}\right|=6

and

\left|\overset{\rightarrow}{c}\right|=14

[NDA II 2016]

© examsnet.com

Question : 67 of 120

Marks: +1, -0

\; \text{ What is } \; \vec{a} \cdot \vec{b} + \vec{b} = \vec{c} + \vec{c} \cdot \vec{a} \; \text{ equal to? } \;

$-332$
$-166$
0
166

Solution:

We have

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

So

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

\Rightarrow |\vec{a}+\vec{b}+\vec{c}|^{2} = |\vec{a}|^{2} + |\vec{b}|^{2} + |\vec{c}|^{2} + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})

\Rightarrow 0 = (10)^2 + (6)^2 + (14)^2 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})

\Rightarrow 0 = 100 + 36 + 196 + 2(\vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a})

\Rightarrow \frac{-332}{2} = \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}

\Rightarrow -166 = \vec{a} \cdot \vec{b} + \vec{b} \cdot \vec{c} + \vec{c} \cdot \vec{a}

© examsnet.com

Go to Question:

Prev Question

Next Question