Question

(3x-4y+z)2-(x-2y–z)?​

Answer 1

Answer:

Those who want complicated solutions are disappointed by the simple solution offered by the other two answers. Here we go .

x+2y+2z=0(1)

3x−4y+z=0(2)

These two are equations of planes passing through (0,0,0)

the intersection is a line whose direction ratios are given by

∣∣∣∣i13j2−4k21∣∣∣∣

i.e10i^+5j^−10k^⟹2i^+j^−2k^

The equation of line of intersection is

x2=y1=z−2=t where t is a parameter.⟹

x=2t;y=t;z=−2t.

Now we shall find intersection of this line with the curve.

x2+3y2+z2=11(3)

4t2+3t2+4t2=11⟹t2=1;t=±1

So the two points of intersection are

(2,1,−2),(−2,−1,2