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Standard XII

Mathematics

Representation of Vectors

The component...

Question

The components of a vector along $x$ and $y$ directions are $(n + 1)$ and $1$ respectively. If the coordinate system is rotated by an angle $60^{\circ}$ , then the components change to $n$ and $3$ . The value of $n$ is

2

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3

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0.5

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3.5

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Solution

The correct option is D $3.5$
Rotation of the coordinate axes doesnot change the length of the vector. So,

$\sqrt{(n + 1)^{2} + 1^{2}} = \sqrt{n^{2} + 3^{2}}$
$n^{2} + 2 n + 2 = n^{2} + 9$
$2 n = 7$
$n = 3.5$

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The components of a vector along x and y directions are (n+1) and 1 respectively. If the coordinate system is rotated by an angle 60∘, then the components change to n and 3. The value of n is

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The components of a vector along $x$ and $y$ directions are $(n + 1)$ and $1$ respectively. If the coordinate system is rotated by an angle $60^{\circ}$ , then the components change to $n$ and $3$ . The value of $n$ is

The correct option is D $3.5$
Rotation of the coordinate axes doesnot change the length of the vector. So,

$\sqrt{(n + 1)^{2} + 1^{2}} = \sqrt{n^{2} + 3^{2}}$
$n^{2} + 2 n + 2 = n^{2} + 9$
$2 n = 7$
$n = 3.5$