Motion in a Plane - Result Question 15
17. If a unit vector is represented by $0.5 \hat{i}+0.8 \hat{j}+c \hat{k}$, the value of $c$ is
[1999]
(a) 1
(b) $\sqrt{0.11}$
(c) $\sqrt{0.01}$
(d) 0.39
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Answer:
Correct Answer: 17. (b)
Solution:
- (b) $\hat{r}=0.5 \hat{i}+0.8 \hat{j}+c \hat{k}$
$|\hat{r}|=1=\sqrt{(0.5)^{2}+(0.8)^{2}+c^{2}}$
$(0.5)^{2}+(0.8)^{2}+c^{2}=1$
$c^{2}=0.11 \Rightarrow c=\sqrt{0.11}$
Unit vector is a vector which has a magnitude of one. It is a vector divided by its magnitude. Unit vector for
$\vec{A}$ is $\hat{A}: \hat{A}=\frac{\vec{A}}{A}$
Unit vector gives direction.
