What is the general equation of the plane containing the lines l1 and l2?

x+y+z=0.

What is a vector plane?

Vector Representation A vector in a plane is represented by a directed line segment (an arrow). The endpoints of the segment are called the initial point and the terminal point of the vector. An arrow from the initial point to the terminal point indicates the direction of the vector.

How do you write a vector equation of a plane?

The equation of a plane in vector form can be written as ⃑ 𝑛 ⋅ ⃑ 𝑟 = ⃑ 𝑛 ⋅ ⃑ 𝑟 ,  with ⃑ 𝑟 = ( 𝑥 , 𝑦 , 𝑧 ) and ⃑ 𝑟  as the position vector of a point that lies on the plane.

What is a vector of a plane?

A vector in a plane is represented by a directed line segment (an arrow). The endpoints of the segment are called the initial point and the terminal point of the vector. An arrow from the initial point to the terminal point indicates the direction of the vector.

How do you find the plane perpendicular to a vector?

A plane defined via vectors perpendicular to a normal. Thus, given a vector ⟨a, b, c⟩ we know that all planes perpendicular to this vector have the form ax + by + cz = d, and any surface of this form is a plane perpendicular to ⟨a, b, c⟩ . Example 12.5.1 Find an equation for the plane perpendicular to ⟨1, 2, 3⟩ and containing the point (5, 0, 7) .

How to find the intersection line equation between two planes?

Find the intersection line equation between the two planes: 3x − y + 2z − 4 = 0 and 2x − y + 4z − 3 = 0 Any point on the intersection line between two planes satisfies both planes equations. But because we have three unknowns and only two equations, we can choose one variable value for example z = t then we get the equations:

How to find the intersection line by vector method?

The intersection line can also be found by vector method. The general vector direction of the perpendicular lines to the first and second planes are the coefficients x, y and z of the planes equations.

How do you find the vector equation for a line?

The vector equation for any line is $$r(t) = ext{point you want it to pass through} + ext{parameter} \\cdot ext{velocity vector}.$$ You want it to pass through the point $P = (-1,-5,2)$ and uses the parameter $t$, so we write