Show that the line of intersection between 1 and 3 is parallel to the line of intersection of2 and 3. Consult Section 1.2 for the definition of parallel lines in 3. 1.2 Section SummaryThe equation that we obtained, 7x+ 17y- 2z = 0, is called a Cartesian equation for thisplane. Thus, we can summarize this Example by saying:The Span of a non-empty set of vectors S = {v1, v2, ..., v} from R" is the set of all possiblelinear combinations of the vectors in the set. We write:If i = (3,-1, 2), and v = (-4, 2, 3), then:Span(S) = Span({vi, v2, ..., va} )Span({i, v}) is the plane with Cartesian equation: 7x + 17y – 2z = 0.0= {xiv1 +x2v2 + ...+xVk |X1, x2, ..., x e R}.We note that the individual vectors v1, v2, ..., V are all members of Span(S), where we letX; = 1 and all the other coefficients 0 in order to produce v. Similarly, the zero vector 0, isalso a member of Span(S), where we make all the coefficients zero to produce 0,.We generalize this Example in the following:Definition – Axiom for a Plane in Cartesian Space:If i and v are vectors in R3 that are not parallel to each other, then Span({ủ, v}) isgeometrically a plane II in Cartesian space that passes through the origin. It has aCartesian equation, of the form:1.2.1: In any R": Span ({0,}) = {0,}.1.2.2: For all vi, v2, ..., Vk e R": Span ({0n, V1, v2, ..., V}) = Span ({v1, v2, .., va }).ax + by + cz = 0,If v e R" is a non-zero vector, then Span({v}) is geometrically a line L in R" passing throughthe origin.for some constants, a, b and c, where at least one coefficient is non-zero.In particular, if we write v = (a, b, c) e R³, then L = Span({v}) has vector equation:The letter II is the capital form of the lowercase Greek letter t.In other words, there exist scalars a, b, and c, not all zero, such that:(x, y, z) = t(a, b, c), where t e R.(x, y, z) e Span({i, v}) if and only if ax + by + cz = 0.This can be rewritten into parametric equations:x = at, y = bt, and z = ct, where t e R.1.2.3: If i andv are non-zero and parallel vectors from some R", then:Span({i, v}) = Span({v}) = Span({ū}),which is still a line L passing through the origin.1.2.4: If i, v e R² are non-parallel vectors, then: Span({ủ, v}) = R².In other words, any vector w = (x, y) e R2 can be expressed as a linear combination:w = rủ + sv, for some scalarsr and s.The Span of Two Non-Parallel Vectors in R3 is a Plane Through the OriginAxiom for a Plane in Cartesian Space:If i and v are vectors in R3 that are not parallel to each other, then Span({i, }) isgeometrically a plane II in Cartesian space that passes through the origin. It has a Cartesianequation, in the form:The Cartesian equation of a plane in R3 is not unique. In our Example, the Cartesian equation:- 21x – 5ly + 6z = 0ax + by + cz = 0,will represent exactly the same plane 7x+ 17y- 2z = 0, since we multiply the originalequation by -3 to get the new equation. Since we can do this with any non-zero scalar, thereare an infinite number of Cartesian equations for this plane.for some constants, a, b and c, where at least one coefficient is non-zero.In other words, there exist scalars a, b, and c, not all zero, such that a vector(x, y, z) e Span({ū,v}) if and only if ax + by + cz = 0. 10. Suppose that II1 and II2 are parallel planes in R³, given by:II1 : ajx + b¡y+cjz = d1, and II2 : ajx + b¡y+cjz = d2,where di + d2. Now, suppose that II3 is another plane given by:d3,II3 : a3x + b3y + C3z||which is not parallel to II1 or II2. Show that the line of intersection between II, and II3is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definitionof parallel lines in R³.

Question

Show that the line of intersection between 1 and 3 is parallel to the line of intersection of2 and 3. Consult Section 1.2 for the definition of parallel lines in 3. 1.2 Section SummaryThe equation that we obtained, 7x+ 17y- 2z = 0, is called a Cartesian equation for thisplane. Thus, we can summarize this Example by saying:The Span of a non-empty set of vectors S = {v1, v2, ..., v} from R&#34; is the set of all possiblelinear combinations of the vectors in the set. We write:If i = (3,-1, 2), and v = (-4, 2, 3), then:Span(S) = Span({vi, v2, ..., va} )Span({i, v}) is the plane with Cartesian equation: 7x + 17y – 2z = 0.0= {xiv1 +x2v2 + ...+xVk |X1, x2, ..., x e R}.We note that the individual vectors v1, v2, ..., V are all members of Span(S), where we letX; = 1 and all the other coefficients 0 in order to produce v. Similarly, the zero vector 0, isalso a member of Span(S), where we make all the coefficients zero to produce 0,.We generalize this Example in the following:Definition – Axiom for a Plane in Cartesian Space:If i and v are vectors in R3 that are not parallel to each other, then Span({ủ, v}) isgeometrically a plane II in Cartesian space that passes through the origin. It has aCartesian equation, of the form:1.2.1: In any R&#34;: Span ({0,}) = {0,}.1.2.2: For all vi, v2, ..., Vk e R&#34;: Span ({0n, V1, v2, ..., V}) = Span ({v1, v2, .., va }).ax + by + cz = 0,If v e R&#34; is a non-zero vector, then Span({v}) is geometrically a line L in R&#34; passing throughthe origin.for some constants, a, b and c, where at least one coefficient is non-zero.In particular, if we write v = (a, b, c) e R³, then L = Span({v}) has vector equation:The letter II is the capital form of the lowercase Greek letter t.In other words, there exist scalars a, b, and c, not all zero, such that:(x, y, z) = t(a, b, c), where t e R.(x, y, z) e Span({i, v}) if and only if ax + by + cz = 0.This can be rewritten into parametric equations:x = at, y = bt, and z = ct, where t e R.1.2.3: If i andv are non-zero and parallel vectors from some R&#34;, then:Span({i, v}) = Span({v}) = Span({ū}),which is still a line L passing through the origin.1.2.4: If i, v e R² are non-parallel vectors, then: Span({ủ, v}) = R².In other words, any vector w = (x, y) e R2 can be expressed as a linear combination:w = rủ + sv, for some scalarsr and s.The Span of Two Non-Parallel Vectors in R3 is a Plane Through the OriginAxiom for a Plane in Cartesian Space:If i and v are vectors in R3 that are not parallel to each other, then Span({i, }) isgeometrically a plane II in Cartesian space that passes through the origin. It has a Cartesianequation, in the form:The Cartesian equation of a plane in R3 is not unique. In our Example, the Cartesian equation:- 21x – 5ly + 6z = 0ax + by + cz = 0,will represent exactly the same plane 7x+ 17y- 2z = 0, since we multiply the originalequation by -3 to get the new equation. Since we can do this with any non-zero scalar, thereare an infinite number of Cartesian equations for this plane.for some constants, a, b and c, where at least one coefficient is non-zero.In other words, there exist scalars a, b, and c, not all zero, such that a vector(x, y, z) e Span({ū,v}) if and only if ax + by + cz = 0. 10. Suppose that II1 and II2 are parallel planes in R³, given by:II1 : ajx + b¡y+cjz = d1, and II2 : ajx + b¡y+cjz = d2,where di + d2. Now, suppose that II3 is another plane given by:d3,II3 : a3x + b3y + C3z||which is not parallel to II1 or II2. Show that the line of intersection between II, and II3is parallel to the line of intersection of II2 and II3. Consult Section 1.2 for the definitionof parallel lines in R³.

Accepted Answer

Given two plane which are parallel 
Π1:a1x+b1y+c1z-d1,  Π2:a2x+b2y+c2z-d2
and another plane is…