Latest TCS Aptitude Question SOLUTION: What is the distance between point in z-axis from point in x-axis, where given plane ax+by+cz+d=0 intercept.

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What is the distance between point in z-axis from point in x-axis, where given plane ax+by+cz+d=0 intercept.

Asked In TCS NISHANT SRIVASTAVA (13 years ago)

Solved Ranjeet Verma Read Solution (9)

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Read Solution (9) :

Somil Nain  (13 years ago)

sqrt{(-d/c)^2+(-d/a)^2}

Is this solution Helpfull? Yes (66) | No (6)  

dhiresh  (13 years ago)

equa is ax+by+cz+d=0 put the x=0 ,y=0 for finding z co-ordinate
now put the y=0,z=0 for finding x co-ordinate now for distance apply the distance formula..D=root(square(x1-x2)+square(y1-y2)+square(z1-z2))

Is this solution Helpfull? Yes (59) | No (9)  

Ranjeet Verma  (13 years ago)

by putting y=z=0 in equation we get coordinate of x((-d/a),0,0)
x=z=0 coordinate of y(0,(-d/b),0) and x=y=0 coordinate of z(0,0,(-d/c))
sqrt{(-d/a)^2)+((-d/c)^2)}=d*sqrt((1/a^2)+(1/c^2))

Is this solution Helpfull? Yes (38) | No (10)  

sumit   (13 years ago)

ax+by+cz=-d
x/(-ad)+y/(-bd)+z/(-cd)=1
x-intercept=ad
z-intercept=cd
distance between these two=(ad^2+cd^2)^(1/2)

Is this solution Helpfull? Yes (8) | No (19)  

nishant nandan  (13 years ago)

make the equation as ax+by+cz=-d.furter divide the terms by -d to make rhs 1.take the coefficient of x and z and subtract it.thats the ans

Is this solution Helpfull? Yes (4) | No (6)  

Sharda Prasad Jaiswal  (13 years ago)

The plane crosses the x axis when y = z = 0; similarly x = y = 0 when it crosses the z-axis. We have to make some assumptions about the coefficients a and c---namely that they are not zero so that the plane does actually cross these axes. (Well, there is the other degenerate case in which the plane is the xz-plane y = 0.)
If a and c are nonzero, the intersection of the plane with the x-axis occurs at the point (-d/a,0,0) and that with the z-axis occurs at (0,0,-d/c). The distance between these points is
√((-d/a)^2 + (-d/c)^2) = |d|/√(a^2 + c^2)

Is this solution Helpfull? Yes (4) | No (6)  

veerbahadur gupta  (13 years ago)

change it in the form of...
x/a+y/b+z/c=1....
u wil get the ans...

Is this solution Helpfull? Yes (3) | No (7)  

PANDU RANGA RAO  (12 years ago)

for the answer we divide equation with d then we get individual terms
then answer is sqrt(d^2/(a^2+c^2))

Is this solution Helpfull? Yes (1) | No (6)  

Akrati Soni  (7 years ago)

d/((x-a)^2+(z-c)^2)1/2

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