    Question

# Which of the following is a unit vector in the direction of ^i+^j+^k.

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D
None of these
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Solution

## The correct option is C Magnitude of (^i+^j+^k)=√12+12+12=√3 Now from scalar multiplication of vectors, we know that if we multiply a vector with a positive scalar, its direction remains unchanged, but its magnitude changes. So if I multiply ^i+^j+^k by 1√3, what will be its magnitude? Let’s check the magnitude of ^i√3+^j√3+^k√3=√(1√3)2+(1√3)2+(1√3)2=1 Now this has magnitude 1 with the direction same as that of ^i+^j+^k Why the directions of ^i√3+^j√3+^k√3 and ^i+^j+^k are same? Because they are just scalar multiples of each other. And scalar multiplication does not change the direction of a vector but only changes its magnitude. So ^i√3+^j√3+^k√3 is a unit vector in the direction of ^i+^j+^k. I have done nothing, just divided the vector by its magnitude to make its magnitude = 1, keeping the direction same as that of original vector.  Suggest Corrections  0      Similar questions  Related Videos   Unit Vectors
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