Question

Equation to a line parallel to the vector $2\hat{i}-\hat{j}+\hat{k}$ and passing through the point $\hat{i}+\hat{j}+\hat{k}$

• A. $(x-1)\hat{i}+(y-1)\hat{j}+(z-1)\hat{k}=\lambda (2\hat{i}-\hat{j}+\hat{k})$
• B. $(x-2)\hat{i}+(y-1)\hat{j}+(z+1)\hat{k}=\lambda (\hat{i}+\hat{j}+\hat{k})$
• C. $2x\hat{i}-y\hat{j}+z\hat{k}=\lambda (\hat{i}+\hat{j}+\hat{k})$
• D. $(x-1)\hat{i}+(y+1)\hat{j}+(z+1)\hat{k}=\lambda (\hat{i}+\hat{j}+\hat{k})$

Answer 1

The correct option is A $(x-1)\hat{i}+(y-1)\hat{j}+(z-1)\hat{k}=\lambda (2\hat{i}-\hat{j}+\hat{k})$

Equation parallel to a vector $\overrightarrow{a}$ and passing through point of position vector $\overrightarrow{b}$ is given by $\overrightarrow{r}=\overrightarrow{a}+\lambda \overrightarrow{b}$

$\overrightarrow{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda (2\hat{i}-\hat{j}+\hat{k})$

$x\hat{i}+y\hat{j}+z\hat{k}=\hat{i}+\hat{j}+\hat{k}+\lambda (2\hat{i}-\hat{j}+\hat{k})$
$(x-1)\hat{i}+(y-1)\hat{j}+(z-1)\hat{k}=\lambda (2\hat{i}-\hat{j}+\hat{k})$