2 b) Prove that Imz=0, larg z - 41= 4, 2-ž =0, 1Z-il=1Ztil are different equations all describing the eal (x) axis.

Q: 11) Find the equation of the plane that passes through the point (1, 5, 1) and is perpendicular to…

A: A plane is passing through a point (1,5,1) and is perpendicular to the planes 2x + y - 2z = 2 and x+…

Q: The distance from (6,-5, 1) to yZ-plane is OA 6 /26 OC 1 O D. 62 OE 5 В.

A:

Q: Find the equation for the plane through Po(-6,3,7) perpendicular to the following line. x= -6+t, y…

A:

Q: The plane equation that has 3.9 units distance to the plane 5x -2y + 3z= 4 is O a. 5.0x-4y+3z=56.1 O…

A:

Q: Calculate gij for the distance between (x;) = (1, 1, – 1) and (yi) = (0,1,2) in %3D T-2 1] barred…

A: A point in three dimensional coordinate system is given by xi=1,1,-1yi=0,1,2 Now the point in barred…

Q: Find a parametrization for the line segment beginning at P1 and ending at P2. 25) P1(-4, –5, 4) and…

A:

Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: Find a parametrization of the line through P = (4, 9, 8) perpendicular to the yz-plane.

A: Equation of Linethe Line through P =(x0,y0,z0) in the diresction of vector v→=(a,b,c)is defined…

Q: 9. Compute the distance between the point (-2, 8, 1) and the line of intersection between the two…

A:

Q: 2. Find the distance between the given parallel planes. 2x +y+ 2z = 8 and 4x +2y + 4z +5 = 0

A: # we are entitled to solve one question at a time, please resubmit the other questions if you wish…

Q: 5z' + 3z gral z² - 4 plane, is

A:

Q: What kind of conic section is given by the quadratic form ? -11x,2 + 84x,x2 + 24x,2 = 156 Transform…

A: Given Quadratic Equation is, -11x12+84x1x2+24x22=156 Matrix Representation form is, A=-11424224 Find…

Q: The equation of plane through the origin and parallel to the plane 2x+ 5y – 4z = 8 is 2x + 5y – 4z =…

A:

Q: Find the condition for the points (a,0),(h,k),(0,b) when ais not equals to 0 to be collinear

A:

Q: 5. Consider two distinct points [b1 in the and plane. Explain why the solutions of the equation det…

A:

Q: 7. Show that the equation of the plane that has x-intercept a, y-intercept b, and z-intercept c…

A:

Q: Give equations for two distinct planes whose trace in the yz-plane has equation y = 4z

A: Given, two distinct planes have trace in the yz-plane has equation y = 4z

Q: y -6- 4- 3- 2- 1- -3 2 -1 0 12 3 4 5 6 -1- -2- R -3- your work on question 10, classify this…

A:

Q: 3. [For students with ID # ending in 4 or 5.] Through the point (4, 2, -5) and perpendicular to the…

A: Here, the given equation of the plane is 3x+y-6z=8 So, the coefficients of x,y and z will give us…

Q: Find the equation of the plane which passes through O and is parallel (5а + бу) — 3 to z – %3D

A: The equation of given plane is,      z - (5x + 6y) = 3⇒ z - 5x - 6y = d   for a plane of the form ax…

Q: z= 2e'+i

A:

Q: The plane equation that has 2.5 units distance to the plane 5x- 2y + 3z = 4 is %3D O a.…

A: Option (d) is correct.

Q: A point moves in the (x, y) plane on the line 2x+ 3y −4 = 0. Where will it be when the sum of the…

A: We have to find a point from where the sum of square of its distances from 1,0 and -1,0 is smallest.

Q: 10. The distance between the point (3,-2,5) and the plane 2x+2y+z=5 is NONE

A: Given: The distance between (3,-2,5) and the plane 2x+2y+z=5

Q: 2. Use analytic geometry to verify that quadrilateral JKLM is a parallelogran 1C). YA K(-1,1) 2 -2 0…

A:

Q: Find the condition for the points (a, 0), (h, k), (0, b)when ais not equals to U to be collinear

A: We have to find the condition

Q: II. Use Theorem 6.1.1 or Theorem 6.1.2 to solve the following problem: What are the equations of…

A: From the given data, Assuming the illustration in a 2D space. Let P=α,β Then, O be the origin.

Q: Give equations for two distinct planes whose trace in the xy-plane hasequation 4x + 3y = 8.

A: Given information: The xy-plane has equation 4x + 3y = 8. Calculation: The equation of the plane is…

Q: 5. Calculate the distance between the point (3, 1, -2) and the plane 2x + y-2+1. O 10 o -10 V14 O 10…

A: The equation of the plane is  2x+y-z+1 = 0 The point is x0,y0,z0 =3,1,-2 To evaluate : The distance…

Q: 1. Find an equation for the plane through Po (0,2,-1) perpendicular to n = 3i - 2 j- k ?

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: Find 3 non-collinear points in the plane ax+by+cz+d=0. (Hint: Set two variables to zero for each…

A: Since you have asked multiple questions in a single request we would be answering only the first…

Q: Suppose there are two lines in the xy-plane in R^2.  These two lines could intersect at a single…

A: let the lines be                              y=m1x+c1y=m2x+c2 given that lines are intersecting in…

Q: 4) Find the distance from the point (1, 2, – 1) to the plane 2x+y- 2z = 1.

A:

Q: 3. Find how many roots the equation 2z4 – 323 + 3z² – z + 1 = 0 - - has in the right half-plane Rez…

A: Given: 2z4-3z3+3z2-z+1=0

Q: 1) Find the distance from the point (1, 2, 3) (a) XZ plane to the (b) Z axis

A: In this question we will use basic of geometry i.e concept of 3D geometry. We will first plot the…

Q: find the equation of the line through (0,2,1) that is perpendicular to both u= 4i + 3j − 5k and the…

A:

Q: +4z=8 and

A: The equation of the plane as, x+z=1orx+0y+z=1 Here, a1 =1,b1 =0,c1 =1. and x+2y+4z=8 Here, a2 =1,b2…

Q: 12. Find the distance between the point (3,-2,7) and the plane 4x – 6 y + z = 5.

A: The equation of plane is 4x-6y+z=5 and the given point is 3,-2,7. The distance between the point and…

Q: Find the distance from the point (5, 4, 3) to the plane −4x−1y−1z=4.

A:

Q: The plane containing the point (-4,1,3) and parallel to the plane 4x + 7y – 3z = 2 has equation Ar +…

A:

Q: Determine the set of points satisfying the condition described by |z – 3| + |z + 3| = 10 Then…

A:

Q: (2, 1) is the midpoint of AB, in which A has coordinates (8, 10). Find the coordinates of B.

A: given: (2,1) is the mid point of AB. the coordinates of A are (8,10) we have to find the coordinates…

Q: Use Green's Theorem to evaluate $4x²ydx+2ydy where C is the triangle with vertices (0,0), (1,2), and…

A:

Q: Find the distance between the point (1,3,-1) and the plane 3x - 4y + 5z = 6. (Enter an exact answer…

A: Given point 1,3,-1 and the plane 3x-4y+5z=6

Q: The distance from (10,-9,5) to yZ-plane is - 10 B.9 OC.5 OD. 206 OE. /106

A: We will find the distance between the point and the yz plane as following.

Q: ind the equation of the parabora y= ax^2 +bx +c that passes through points (0,3) (1,-4) (-1,4)

A: Consider the equation of parabola is given as in the question and passing through the points (0, 3)…

Q: Find the set of points that is satisfied the condition described by |z – 2i|+ |z + 4i| = 10

A:

Q: The distance between the centers of the following two spheres: x2+56x+y2−54y+z2=−1512,…

A: A detailed solution is given below

Percentage

A percentage is a number indicated as a fraction of 100. It is a dimensionless number often expressed using the symbol %.

Algebraic Expressions

In mathematics, an algebraic expression consists of constant(s), variable(s), and mathematical operators. It is made up of terms.

Numbers

Numbers are some measures used for counting. They can be compared one with another to know its position in the number line and determine which one is greater or lesser than the other.

Subtraction

Before we begin to understand the subtraction of algebraic expressions, we need to list out a few things that form the basis of algebra.

Addition

Before we begin to understand the addition of algebraic expressions, we need to list out a few things that form the basis of algebra.