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 State True or False for the given statement.

The vector equation of the line \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2} is   r=5\hat{i}-4\hat{j}+6\hat{k}+\lambda\left ( 3\hat{i}+7\hat{j}+2\hat{k} \right )

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The given equation of the line is  \frac{x-5}{3}=\frac{y+4}{7}=\frac{z-6}{2}

It is clear from the equation that this line passes through A (5, -4, 6) and has the direction ratios 3, 7 and 2.

The position vector of A is \vec{a}=5\hat{i}-4\hat{j}+6\hat{k}

And the direction vector of the line will be

We know, the vector equation of a line that passes through a given point with position vector a and b is given as


Hence, the required line equation will be:

\hat{r}=\left ( 5\hat{i}-4\hat{j}+6\hat{k}\right )\lambda\left ( 3\hat{i}+7\hat{j}+2\hat{k} \right )

Thus, the statement is True.

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