Question

The components of a vector along the x-and y-
directions are (n + 1) and 1, respectively. If the
coordinate system is rotated by an angle 0 = 60°,
then the components change to n and 3. The value
of n is​

Answer 1

Answer:

Let the vector be p with magnitude p , making an angle x with x-axis.

The components as given in question can be rewritten as:-

p cosx = n+1

p sinx = 1

Now, the coordinate system is rotated by 60 degrees. It can be clockwise or anticlockwise. Accordingly, the angle changes either to x+60 or x-60.

The final components system is :-

p cosx(x+/- 60)=n

p sin(x+/-60)=3

Using these 4 equations, n can be easily found.

Say, lets open p cosx(x+/-60)=n

p[cos x . Cos60 -/+ sin x . Sin60]=n

Substituting cos 60=1/2, sin60= (√3)/2, p cos x= n+1, p sin x=1,

Explanation:

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Answer 2

Answer:

$\frac{7}{2}$

Explanation:

$\sqrt{ {(n + 1)}^{2} + {1}^{2} } = \sqrt{ {x }^{2} + {3}^{2} }$

Squaring on both sides:

${(x + 1)}^{2} + {1}^{2} = {x}^{2} + 9$

${x}^{2} + 1 + 2x + 1 = {x}^{2} + 9$

$2x = 7$

$x = \frac{7}{2}$

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