Question

Find the equation of the plane passing through (a, b, c) and parallel to the plane $\vec r.(\hat i+\hat j+\hat k)=2$.

Answer 1

Solution:

Any plane which is parallel to the plane
$\vec r.(\hat i+\hat j+\hat k)=2$

is given by

$\vec r.(\hat i+\hat j+\hat k)=q$

for some constant q.

Now to find the value of q,since that plane passes through point (a,b,c) whose position vector is

$(a\hat i+b\hat j+c\hat k)$

we have

$(a\hat i+b\hat j+c\hat k).(\hat i+\hat j+\hat k)=q\\\\q=(a+b+c)$

So, vector equation of that plane is

$\vec r.(\hat i+\hat j+\hat k)=(a+b+c)$

Hope it helps you.