Write down a unit vector in …
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Posted by Chetan Kumar 5 years, 10 months ago
- 1 answers
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Gaurav Seth 5 years, 10 months ago
Let the unit vector is a in XY-plane
So a = xi + yj .............1
where unit vector in the direction of x-axis is i and in y-axis is j
Now given that a makes an angle of 30 with x-axis
So a.i = |a|*|i|*cos 30
=> a.i = 1*1*√3/2 (since a and i are unit vector so |a| = 1, |i| = 1 )
=> a.i = √3/2
=> (xi + yj + 0k).(1i + 0j + 0k) = √3/2
=> x = √3/2 (i.i = j.j = k.k = 1)
Again since a makes an angle of 30 with x-axis then a makes an angle of 60 with y-axis
So a.j = |a|*|j|*cos60
=>(xi + yj + 0k).(0i + 1j + 0k) = 1/2
=> y = 1/2
Now put value of x and y in equation 1, we get
a = (√3/2)i + (1/2)j
So unit vector is (√3/2)i + (1/2)j
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