Question

The rectangular components of a vector lying in XY plane are ( N +2) and 1. If the coordinate system is turned by 300, they become N and 4. The value of N is
1.7/4
2.4/11
3.4/7
4.11/4
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Answer 1

Answer:

3

Explanation:

4/7 ..............,

Answer 2

Answer:

The value of N is 11/4.

Explanation:

Given:

Rectangular component of vector in XY plane are (N + 2) and 1.

After turning the coordinate system by 300, they become N and 4.

We have to find the value of N.

Now we know that, when the coordinate system is turned by any degree the magnitude of the vector before turning ang after turning the plane remains the same.

Initial magnitude of the vector is given by:

⇒ $\sqrt{(N+2)^2+1^2}$

⇒ $\sqrt{N^2+4N+4+1}$

⇒ $\sqrt{N^2+4N+5}$                          …(1)

Magnitude of the vector after turning the coordinate system is given by:

⇒ $\sqrt{N^2+4^2}$

⇒ $\sqrt{N^2 +16}$                                 …(2)

Now, we will equate both the equations (1) and (2), we get:

⇒ $\sqrt{N^2+4N+5}=\sqrt{N^2+16}$

Now, squaring on both the sides we get:

⇒ N² + 4N + 5 = N² + 16

⇒ 4N = 16 - 5

⇒ 4N = 11

⇒ N = 11/4

Therefore, the value of N is 11/4.

Hence, option (4) is correct.