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Standard XII

Mathematics

Equal 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 angle 60° then the components change to n and 3. The value of n is . (A)2 (B)cos60 (C)sin60 (D) 3.5

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Solution

Dear student,

Rotation does not change the magnitude (length) of a vector so:
√[(n+1)² +1²] = √[n² +3²]
(n+1)² +1 = n² + 9
n² + 2n + 2 = n² + 9
2n = 7
n = 3.5

Regards

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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 angle 60° then the components change to n and 3. The value of n is . (A)2 (B)cos60 (C)sin60 (D) 3.5

Dear student, Rotation does not change the magnitude (length) of a vector so: √[(n+1)² +1²] = √[n² +3²] (n+1)² +1 = n² + 9 n² + 2n + 2 = n² + 9 2n = 7 n = 3.5 Regards

Dear student,

Rotation does not change the magnitude (length) of a vector so:
√[(n+1)² +1²] = √[n² +3²]
(n+1)² +1 = n² + 9
n² + 2n + 2 = n² + 9
2n = 7
n = 3.5

Regards