Question

direction of the line perpendicular to the plane 3x-4y+7z=2 and passing through (-1,2,4) is ____​

Answer 1

Step-by-step explanation:

Given,

$\large{\tt{\bold{Equation\:\:of\:\:Plane:}}}\:3x-4y+7z=2$

In vector form we have,

$\vec{r}.(3 \hat{i} - 4 \hat{j} + 7\hat{k}) = 7$

This is in the form of $\vec{r}.\vec{n}=d$, where, $\vec{n}=3\hat{i}-4\hat{j}+7\hat{k}$

The line perpendicular to the given plane will be parallel to $\vec{n}$

Let, the required vector be $\vec{r}=x\hat{i}+y\hat{j}+z\hat{k}$,

Also,

It passes through $(-1,2,4)$

So,

$\vec{r} = (- \hat{i} + 2\hat{j} + 4 \hat{k} )+ \lambda(3 \hat{i} - 4 \hat{j} + 7 \hat{k})$

Answer 2

Answer:

Step-by-step explanation: