Question

Find the Cartesian form of the equation of a plane whose vector equation is

i. r.(12i - 3j + 4k) + 5 = 0

ii. r.(-i + j + 2k) = 9

Answer 1

i. \(\vec r.(12\hat i - 3\hat j + 4\hat k)+5=0\)

Given the vector equation of a plane,

Then, the given vector equation becomes,

Now multiplying the two vectors using the formula

We get

This is the Cartesian form of equation of a plane whose vector equation is

ii. \(\vec r.(-\hat i +\hat j + 2\hat k)=9\)

Given the vector equation of a plane,

Then, the given vector equation becomes,

Now multiplying the two vectors using the formula

We get

This is the Cartesian form of equation of a plane whose vector equation is