Latest TCS Aptitude Question SOLUTION: what is the distance between the z-intercept from the x0intercept in the equation ax+by+cz+d=0.

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what is the distance between the z-intercept from the x0intercept in the equation ax+by+cz+d=0.

Asked In TCS xyz (12 years ago)

Solved Siddharth Read Solution (2)

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Siddharth  (12 years ago)

z-intercept, z2= -d/c, x2=0, y2=0
& x-intercept, x1= -d/a, y1=0, z1=0
distance between z and x, D = [(x2-x1)^2+(y2-y1)^2+(z2-z1)^2)]^1/2
= [(d/a)^2+(-d/c)^2]^1/2
= d/ac[a^2+c^2]^1/2

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Pushpesh kumar  (11 years ago)

ax + by + cz + d = 0
At the z-intercept, 'x' and 'y' are both zero.
cz + d = 0 --> z = -d/c --> The z-intercept is the point (0, 0, -d/c).
At the x-intercept, 'y' and 'z' are zero.
ax + d = 0 --> x = -d/a --> The x-intercept is the point (-d/a, 0, 0).
The distance between the points (0, 0, -d/c) and (-d/a, 0, 0) is
sqrt[ (-d/a)2 + (-d/c)2 ] = sqrt (d2/a2 + d2/c2) = d sqrt(1/a2 + 1/c2)

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