Misc 1 - Write down a unit vector in XY-plane, making angle 30 - Unit vector

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  1. Chapter 10 Class 12 Vector Algebra
  2. Serial order wise
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Misc 1 Write down a unit vector in XY-plane, making an angle of 30 with the positive direction of x-axis. Let the unit vector be We know that = + y + z Since the vector is in X-Y plane, there is no z coordinate. Hence, = x + y + 0 = + y Unit vector in direction of x axis is & in y axis is Given that makes an angle of 30 with x-axis So, angle between & is 30 Now, we know that, . = cos , Putting = , = & = 30 . = cos 30 . = 1 1 3 2 . = 3 2 ( + y + 0 ). = 3 2 ( + y + 0 ). (1 + 0 + 0 ) = 3 2 .1 + y.0 + 0.0 = 3 2 = Similarly, makes an angle of 60 with y-axis So, angle between & is 60 Now, we know that, . = cos , Putting = , = & = 60 . = cos 60 . = 1 1 1 2 . = 1 2 ( + y + 0 ). = 1 2 ( + y + 0 ). (0 + 1 + 0 ) = 1 2 .0 + y.1 + 0.0 = 1 2 y = Thus, = + y = +

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