$\vec{c}$ is a unit vector in the direction of the sum of vectors $\vec{a}$ and $\vec{b}$. Where,$\vec{a} = 2 \hat{i} + 2 \hat{j} - 5 \hat{k}$ and $\vec{b} = 2 \hat{i} + \hat{j} + 3 \hat{k}$,then $|\vec{c}| = $ . . . . . . .
- A$\frac{4}{\sqrt{29}} \hat{i} + \frac{3}{\sqrt{29}} \hat{j} - \frac{2}{\sqrt{29}} \hat{k}$
- B$0$
- C$1$
- D$-1$
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View SolutionThree non-zero non-collinear vectors $\vec{a}, \vec{b}$ and $\vec{c}$ are such that $\vec{a}+3\vec{b}$ is collinear with $\vec{c}$, and $3\vec{b}+2\vec{c}$ is collinear with $\vec{a}$. Then $\vec{a}+3\vec{b}+2\vec{c}$ equals to
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