A) 1
B) \[\sqrt{0.11}\]
C) \[\sqrt{0.01}\]
D) 0.39
Correct Answer: B
Solution :
| Key Idea: Modulus of unit vector is 1. |
| Let we represent the unit vector by \[\hat{n}\]. We also know that the modulus of unit vectors is 1 i.e., \[|\hat{n}|=1\] |
| \[\therefore \] \[|\hat{n}|=|0.5\,\hat{i}+0.8\,\hat{j}\,+\,c\hat{k}|=1\] |
| or \[\sqrt{{{(0.5)}^{2}}+{{(0.8)}^{2}}+{{c}^{2}}}=1\] |
| or \[0.25+0.64+{{c}^{2}}=1\] |
| or \[0.89+{{c}^{2}}=1\] |
| or \[{{c}^{2}}=1-0.89=0.11\] |
| \[\therefore \] \[c=\sqrt{0.11}\] |
| Note: In the given unit vector \[\hat{i},\,\hat{j}\] and \[\hat{k}\] are orthogonal unit vectors in mutually perpendicular directions. |
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