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Question
Can you add three unit vectors to get a unit vector? Does your answer change if two unit vectors are along the coordinate axes?
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Solution
Yes we can add three unit vectors to get a unit vector.
No, the answer does not change if two unit vectors are along the coordinate axes. Assume three unit vectors \[\hat{i,} - \hat { i} \text { and }\hat { j}\] along the positive x-axis, negative x-axis and positive y-axis, respectively. Consider the figure given below:
The magnitudes of the three unit vectors ( \[\hat {i,} - \hat { i }\text { and } \hat {j})\] are the same, but their directions are different.
So, the resultant of \[\hat { i} \text { and } - \hat {i}\] is a zero vector.
Now, \[\hat {j} + \vec{0} = \hat {j}\] (Using the property of zero vector)
∴ The resultant of three unit vectors ( \[\hat{i,} - \hat {i} \text { and }\hat { j }\]) is a unit vector (\[\hat {j}\]).
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