Test Index

UPSC NDA Math Model Paper 8

Show Para Hide Para

Comprehension:(Que No. 85 - 88)

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

such that

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

and

|\vec{c}|=7

© examsnet.com

Question : 86 of 120

Marks: +1, -0

What is

\vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}

equal to?

-83
-83 / 2
75
-75 / 2

Solution:

Here,

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

and

|c|^{\rightarrow}=7

We have,

|\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{a}\cdot\vec{c})

\therefore |\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{a}\cdot\vec{c})

\Rightarrow 0-3^{2}-5^{2}-7^{2}= 2(\vec{a}\cdot\vec{b}

+\vec{b}\cdot\vec{c}+\vec{a}\cdot\vec{c})

\Rightarrow \vec{a}\cdot\vec{b}+\vec{b}\cdot\vec{c}+\vec{c}\cdot\vec{a}=-\frac{83}{2}

Hence, option (2) is correct.

© examsnet.com

Go to Question:

Prev Question

Next Question