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Study Stuff for MCA Examinations - NIMCET
Study Stuff for MCA Examinations - NIMCET
Previous Year Question (PYQs)
The equation of the plane passing through the point $(1,2,3)$ and having the normal vector
$N = 3\mathbf{i} - \mathbf{j} + 2\mathbf{k}$ is:
Solution
Equation of plane with normal $(a,b,c)$ passing through $(x_1, y_1, z_1)$ is:$a(x - x_1) + b(y - y_1) + c(z - z_1) = 0$
Here:
$a = 3; b = -1; c = 2$
$(x_1, y_1, z_1) = (1,2,3)$
So:
$3(x - 1) - 1(y - 2) + 2(z - 3) = 0$
Expand:
$3x - 3 - y + 2 + 2z - 6 = 0$
Combine constants:
$3x - y + 2z - 7 = 0$
$3x - y + 2z = 7$
Thus the correct answer is:
$3x - y + 2z = 7$
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