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If $0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}}$ is a unit vector, then $c$ is
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Verified Answer
The correct answer is:
$\sqrt{0.11}$
$\begin{array}{r}\text { Given, unit vector is } 0.5 \hat{\mathbf{i}}+0.8 \hat{\mathbf{j}}+c \hat{\mathbf{k}} \\ =\frac{1}{2} \hat{\mathbf{i}}+\frac{4}{5} \hat{\mathbf{j}}+c \hat{\mathbf{k}}\end{array}$
$\begin{aligned} & \Rightarrow \quad \sqrt{\left(\frac{1}{2}\right)^2+\left(\frac{4}{5}\right)^2+c^2}=1 \\ & \Rightarrow \quad \frac{1}{4}+\frac{16}{25}+c^2=1 \Rightarrow c^2=\frac{11}{100} \Rightarrow c=\sqrt{0.11}\end{aligned}$
$\begin{aligned} & \Rightarrow \quad \sqrt{\left(\frac{1}{2}\right)^2+\left(\frac{4}{5}\right)^2+c^2}=1 \\ & \Rightarrow \quad \frac{1}{4}+\frac{16}{25}+c^2=1 \Rightarrow c^2=\frac{11}{100} \Rightarrow c=\sqrt{0.11}\end{aligned}$
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