Question

3.Which equation is equivalent to x + 3y – z = 3?

3x + 6y – 3z = 6


2x + 4y – 2z = 8


4x + 12y – 4z = 12


2x + 3y – 4z = 12


4.Which of the following points lies in the plane 3x – 2y + 4z = –12?

(2,–2, 3)

(5, 15, 2)

(4, 16, 2)

(–4, 3,–2)

Answer 1

3. Which equation is equivalent to
`x + 3y- z = 3`

Now multiply both the sides by 4 we get

`4*(x + 3y- z = 3)\\\\\Rightarrow4*(x+3y-z)=4*3\\\\\Rightarrow4x+12y-4z=12\\\\\ \text{Hence the equivalent equation is } 4x+12y-4z=12\\`

4.

We need to find the point which satisfies the given equation

`3x-2y + 4z =-12\\\\\text{Substitute the point (2,-2,3) we get}\\\\3*2-2(-2)+4(3)=6+4+12=22\\ot\equiv -12\\\\\text{Hence this point does not satisfy}\\\\\text{Now check with the point (4,16,2)}\\\\3*4-2*16+4*2=12-32+8=12=True\\\ \text{Hence the required point is} (4,16,2)\\`