InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
A plane passing through the points (0, -1, 0) and (0, 0, 1) and making an angle `(pi)/(4)` with the plane `y-z+5=0`, also passes through the pointA. `(sqrt(2), 1, 4)`B. `(-sqrt(2), 1, -4)`C. `(-sqrt(2), -1, -4)`D. `(sqrt(2), -1, 4)` |
|
Answer» Correct Answer - A Let the equation of plane is `ax+by+cz=d" "…(i)` Since plane (i) passes through the points `(0, -1, 0)` and (0, 0, 1), then -b=d and c = d `:.` Equation of plane becomes `ax-dy+dz=d" "…(ii)` The plane (ii) makes an angle of `(pi)/(4)` with the plane `y-z+5=0.` `"cos"(pi)/(4)=|(-d-d)/(sqrt(a^(2)+d^(2)+d^(2))sqrt(1+1))|` [`because` The angle between the two plances `a_(1)x+b_(1)y+c_(1)z+d=0" and "a_(2)x+b_(2)y+c_(2)z+d=0`is `costheta=|(a_(1)a_(2)+b_(1)b_(2)+c_(1)c_(2))/(sqrt(a_(1)^(2)+b_(1)^(2)+c_(1)^(2))sqrt(a_(2)^(2)+b_(2)^(2)+c_(2)^(2)))|`] `implies(1)/(sqrt(2))=(|2-d|)/(sqrt(a^(2)+2d^(2))sqrt(2))impliessqrt(a^(2)+2d^(2))=|-d|` `impliesa^(2)+2d^(2)=4d^(2)" "["squaring both sides"]` `impliesa^(2)-2d^(2)impliesa=+-sqrt(2)d` So, the Eq. (ii) becomes `+-sqrt(2)x-y+z=1" "...(i)` Now, from options `(sqrt(2), 1, 4)` satisfy the plane `-sqrt(2)x-y+z=1` |
|