121237
Let \(\mathrm{L}_1\left(\right.\) resp. \(\left.\mathrm{L}_2\right)\) be the line passing through \(2 \mathrm{i}-\) \(\mathbf{k}\) (resp. \(2 \mathbf{i}+\mathbf{j}-3 \mathbf{k}\) ) and parallel to \(3 \mathbf{i}-\mathbf{j}+2 \mathbf{k}\) (resp. \(\mathbf{i}-2 \mathbf{j}+\mathbf{k})\). Then the shortest distance between the lines \(L_1\) and \(L_2\) is equal to
121234
The shortest distance of a point from the \(x\)-axis, \(y\)-axis and \(z\)-axis respectively are \(2,3,6\). What is the distance of the point from the origin?
1 \(\frac{7}{\sqrt{2}}\)
2 7
3 11
4 \(\frac{49}{2}\)
Explanation:
B \(\overrightarrow{\mathrm{r}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\)
\(|\overrightarrow{\mathrm{r}}|=\sqrt{4+9+36}=\sqrt{49}=7\)
121237
Let \(\mathrm{L}_1\left(\right.\) resp. \(\left.\mathrm{L}_2\right)\) be the line passing through \(2 \mathrm{i}-\) \(\mathbf{k}\) (resp. \(2 \mathbf{i}+\mathbf{j}-3 \mathbf{k}\) ) and parallel to \(3 \mathbf{i}-\mathbf{j}+2 \mathbf{k}\) (resp. \(\mathbf{i}-2 \mathbf{j}+\mathbf{k})\). Then the shortest distance between the lines \(L_1\) and \(L_2\) is equal to
121234
The shortest distance of a point from the \(x\)-axis, \(y\)-axis and \(z\)-axis respectively are \(2,3,6\). What is the distance of the point from the origin?
1 \(\frac{7}{\sqrt{2}}\)
2 7
3 11
4 \(\frac{49}{2}\)
Explanation:
B \(\overrightarrow{\mathrm{r}}=2 \hat{\mathrm{i}}+3 \hat{\mathrm{j}}+6 \hat{\mathrm{k}}\)
\(|\overrightarrow{\mathrm{r}}|=\sqrt{4+9+36}=\sqrt{49}=7\)
