Question

A plane \[\pi \] makes intercepts \[3\] and \[4\] respectively on z-axis and x-axis. If \[\pi \] is parallel to y-axis, then its equation is
A) \[3x + 4z = 12\]
B) \[3z + 4x = 12\]
C) \[3y + 4z = 12\]
D) \[3z + 4y = 12\]

Answer 1

Hint: With the given intercepts we write a equation of the plane, x by intercepts plus z by intercepts equal to one and taking the L.C.M. of intercepts and multiplying both sides by L.C.M., we get the final equation.



Formula Used:The equation of a plane intercepting lengths \[a,b\] and \[c\] with x-axis, y-axis and z-axis respectively is \[\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1\].



Complete step by step solution:Given that the plane \[\pi \] makes intercepts \[4\] and \[3\] respectively on x-axis and z-axis. That is \[x\]-intercepts(\[a\])\[ = 4\] and \[z\]-intercepts(\[c\])\[ = 3\].
Hence the required equation of the plane is \[\dfrac{x}{4} + \dfrac{z}{3} = 1\]
\[ \Rightarrow 3x + 4z = 12\].



Option ‘A’ is correct



Note: It is noted that the \[x\]-intercepts must be written below the \[x\] and \[z\]-intercepts must be written below the \[z\]. Also taking L.C.M. of the intercepts and after multiplying both sides by L.C.M. we get the final answer.