Question

If the Cartesian equation of a line is $6x-2=3y+1=2z-2$, then the vector equation of the line is

• A. $\overline{r}=(\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}+\hat{k})+\lambda(\hat{i}+2\hat{j}+3\hat{k})$
• B. $\overline{r}=(\hat{i}+\hat{j}+\hat{k})+\lambda(\hat{i}+2\hat{j}+3\hat{k})$
• C. $\overline{r}=(\frac{-1}{3}\hat{i}+\frac{1}{3}\hat{j}+\hat{k})+\lambda(\hat{i}-2\hat{j}+3\hat{k})$
• D. $\overline{r}=(\frac{1}{3}\hat{i}-\frac{1}{3}\hat{j}-\hat{k})+\lambda(\hat{i}-\hat{j}+\hat{k})$

Hint:

Logic Tip: You can find the direction ratios mentally by covering one part of the equality at a time or taking the reciprocals of the variable coefficients. The coefficients are 6, 3, and 2. Their reciprocals are $1/6, 1/3, 1/2$. Multiply by 6 to clear fractions, yielding direction ratios of $1, 2, 3$.

Answer 1

The Correct Option is A