Vectors

Equation of Plane Containing Two Lines

Here you will learn how to find equation of plane containing two lines with examples. Let’s begin – Equation of Plane Containing Two Lines (a) Vector Form If the lines \(\vec{r}\) = \(a_1 + \lambda\vec{b_1}\) and \(\vec{r}\) = \(a_2 + \mu\vec{b_2}\) are coplanar, then \(\vec{r_1}\).(\(\vec{b_1}\times \vec{b_2}\)) = \(\vec{a_2}\).(\(\vec{b_1}\times \vec{b_2}\))  or,   [\(\vec{r}\) \(\vec{b_1}\) \(\vec{b_2}\)] = [\(\vec{a_2}\) …

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Equation of Plane Passing Through Intersection of Two Planes

Here you will learn what is the equation of plane passing through intersection of two planes with examples. Let’s begin – Equation of Plane Passing Through Intersection of Two Planes (a) Vector Form The equation of a plane passing through the intersection of the planes \(\vec{r}.\vec{n_1}\) = \(d_1\)  and \(\vec{r}.\vec{n_2}\) = \(d_2\) is given by …

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Equation of Plane Parallel to Plane

Here you will learn equation of plane parallel to plane with examples. Let’s begin –  Equation of Plane Parallel to Plane (a) Vector Form Since parallel planes have the common normal, therefore equation of a plane parallel to the plane \(\vec{r}\).\(\vec{n}\) = \(\vec{d_1}\) is \(\vec{r}\).\(\vec{n}\) = \(\vec{d_2}\) where \(\vec{d_2}\) is constant determined by the given …

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Angle Between Two Planes Formula

Here you will learn how to find angle between two planes formula with examples. Let’s begin – Angle Between Two Planes Formula The angle between two planes is defined as the angle between their normals. (a) Vector Form The angle \(\theta\) between the planes \(\vec{r}\).\(\vec{n_1}\) = \(\vec{d_1}\) and \(\vec{r}\).\(\vec{n_2}\) = \(\vec{d_2}\) is given by \(cos\theta\) …

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