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Question on vectors.

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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

asked Jul 10, 2017 in Mechanics by shantanupathak (120 points)

1 Answer

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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
answered Sep 19, 2017 by giginailo (2,580 points)
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