Test Index

UPSC NDA I 2014 Mathematics Paper

Show Para Hide Para

For the next two (02) items that follow:

Consider the vectors

\vec{a} = \hat{i} - 2\hat{j} + \hat{k}

and

\vec{b} = 4\hat{i} - 4\hat{j} + 7\hat{k}

[NDA I 2014]

© examsnet.com

Question : 69 of 120

Marks: +1, -0

What is the scalar projection of

\overset{\rightarrow}{a}

\overset{\rightarrow}{b}

1
19/9
17/9
23/9

Solution:

\vec{a}=\hat{i}-2\hat{j}+\hat{k}

and

\vec{a}=4\hat{i}-4\hat{j}+7\hat{k}

\vec{a}\cdot\vec{b}=4+8+7=\sqrt{6}\times\sqrt{65}\cos\theta

\Rightarrow\cos\theta=\frac{19}{\sqrt{6}\times\sqrt{81}}

Scalar projection

=|\vec{a}|\cos\theta=\sqrt{6}\cdot\frac{19}{\sqrt{6}\times9}=\frac{19}{9}

© examsnet.com

Go to Question:

Prev Question

Next Question