The vector R bar = 10i cap + 10j cap. The frame of reference is changed by 30degree anticlockwise. Represent the vector in new co-ordinate system. Plz answer in detail.Thanks

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Given vector is R = 10i + 10j

Consider is sum of two small vectors say a= 10i and b=10j

Then componenting vector a in the new frame of reference we get

10 cos 30° along i and 10sin 30° Along j. Similarly componenting vector b we get

10 cos 30° along j and 10 sin 30°along i.

Therefore,

new a= {(10 root 3)/2} i - {10/2} j

new b= {10/2} i +{(10 root 3) /2} j

So, new R = new a + new b

={(10/2) + (10 root 3)/2} i + {(10 root 3)/2 - (10/2)}j

= 5(1 + root 3) i + 5 (root 3 - 1) j

= 5 x 2.73 i + 5 x 0.73 j

=13.65i +3.65j

Consider is sum of two small vectors say a= 10i and b=10j

Then componenting vector a in the new frame of reference we get

10 cos 30° along i and 10sin 30° Along j. Similarly componenting vector b we get

10 cos 30° along j and 10 sin 30°along i.

Therefore,

new a= {(10 root 3)/2} i - {10/2} j

new b= {10/2} i +{(10 root 3) /2} j

So, new R = new a + new b

={(10/2) + (10 root 3)/2} i + {(10 root 3)/2 - (10/2)}j

= 5(1 + root 3) i + 5 (root 3 - 1) j

= 5 x 2.73 i + 5 x 0.73 j

=13.65i +3.65j

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