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UPSC NDA 2 2016 Mathematics Solved Paper

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

Let

\vec{a} = \hat{i} + \hat{j}, \vec{b} = 3\hat{i} + 4\hat{k}

and

\vec{b} = \vec{c} + \vec{d}

,where

\vec{c}

is parallel to

\vec{a}

and

\vec{d}

is perpendicular to

\vec{a}

[NDA II 2016]

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Question : 66 of 120

Marks: +1, -0

If

\vec{d}=x\hat{i}+y\hat{j}+z\hat{k}

, then which of the following equations is/are correct?

y-x=4

2z-3=0

Select the correct answer using the code given below:

1 only
2 only
Both 1 and 2
Neither 1 nor 2

Solution:

Since

z=4

and

x=\frac{3}{2},y=-\frac{3}{2}

So, neither 1 nor 2 is correct.

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