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Intercept Form of the Equation of the Plane Video Lecture | Mathematics (Maths) Class 12 - JEE
FAQs on Intercept Form of the Equation of the Plane Video Lecture - Mathematics (Maths) Class 12 - JEE
| 1. What is the intercept form of the equation of a plane? |  |
Ans. The intercept form of the equation of a plane is a way to represent the equation using the intercepts on the coordinate axes. It is given by: $\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1$, where $a$, $b$, and $c$ are the intercepts on the $x$, $y$, and $z$ axes, respectively.
| 2. How do I find the intercepts of a plane given its equation? | |
Ans. To find the intercepts of a plane given its equation in intercept form, set any two variables to zero and solve for the third variable. For example, if the equation is $\dfrac{x}{a} + \dfrac{y}{b} + \dfrac{z}{c} = 1$, setting $x = 0$ gives the $y$-intercept as $\left(0, \dfrac{b}{c}, 0\right)$, setting $y = 0$ gives the $x$-intercept as $\left(\dfrac{a}{c}, 0, 0\right)$, and setting $z = 0$ gives the $z$-intercept as $\left(0, 0, \dfrac{c}{a}\right)$.
| 3. Can the intercept form of a plane equation be used for all types of planes? | |
Ans. No, the intercept form of a plane equation is specifically used for planes that intersect the three coordinate axes. It may not be applicable for planes that do not have intercepts on all three axes.
| 4. How is the intercept form related to the standard form of a plane equation? | |
Ans. The intercept form and the standard form of a plane equation are related by a simple algebraic transformation. The standard form of a plane equation is given by $Ax + By + Cz = D$, where $A$, $B$, $C$, and $D$ are constants. To convert from the standard form to the intercept form, divide each term by $D$ to obtain $\dfrac{x}{D/A} + \dfrac{y}{D/B} + \dfrac{z}{D/C} = 1$. Therefore, the intercepts on the coordinate axes are inversely proportional to the constants in the standard form.
| 5. Can the intercept form of a plane equation be used to find the equation of a plane given three points? | |
Ans. No, the intercept form of a plane equation cannot be used directly to find the equation of a plane given three points. For that, other methods such as using the normal vector or cross product are more appropriate. The intercept form is primarily used to represent the equation of a plane in a specific format and to find its intercepts on the coordinate axes.
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