A. Show that the planes (x+ y– z = 1 ) and (2x – 3y+ 4z = 5 ) are neither parallel nor perpendicular.

Q: 20. Find the point at which the line a = 1+ 2t, y = 4t, z = 2 –t intersects the plane r+y – 2z +1=…

A: Given that, equation of line:- x=2t, y=4t, z=2-t Equation of Plane:- x+y-2z+1=0

Q: Find the equation of the plane which passes through O and is parallel to z – (5x + 6y) = 3 x+ y + z…

A: see 2nd step.

Q: 9. Find the equations of the planes that are parallel to 2.x - 2y + z = 5 such that the distance…

A: We will solve the problem.

Q: The diagram approximately Illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 3x+3y+3z+1=0…

A: Given planes are,    x + y + z + 1 = 0  2x + 2y + 2z + 1 = 0  3x + 3y + 3z + 1 = 0    Thus, normals…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0,1,1).

A: First we find out normal vector to the given plane than find out the point that is closed to the…

Q: Find the point on the plane x – 2y + 3z = 6 that is closest to the point (0, 1, 1).

A:

Q: Find the distance between these two planes x + .2y – 2z = 3 and 2x + 4y – 4z = 7 اخترأحد الخيارات a.…

A:

Q: Find the point closest to origin in R³ that is on both the planes 3x+y+z=5 and x+y+z=1.

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

Q: Example 8: Find the point where the line 2t, and z = -3t intersects the plane x = 1 + t, y = –…

A:

Q: Show that the planes given by y − 7z = 16 and 2y − 14z = 5 are parallel, and find the distance…

A:

Q: Find the intersection of the planes x + y + z = 1 and 3x − 2y +z = 5.

A: Consider two planes which are not parallel to each other and intersect. Since planes are three…

Q: The intersection point of the line that passes through the origin and is perpendicular to the plane…

A:

Q: At what point does the line :LiX==€ 1=10+8€ 14. -2y t52 +16:0 10+3€ z=41+3€ intersect with the plane…

A: Question is based on 3d Geometry.

Q: Find the trace of the plane in the given coordinate plane.3x − 9y + 4z = 5,  xz

A: Let the plane P whose equation is:                                          3x-9y+4z=5…

Q: @/ Find the angle between the planes (x-+y+z=1)and (x-2y+32-1). And find the symmetric equations for…

A: Given equations of planes are x+y+z=1 and x-2y+3z=1 Here, a1=1,b1=1,c1=1 & a2=1,b2=-2,c2=3…

Q: Find the point in which the line X = 2, y = 3 + 2t, z = -2 – 2t; meets the plane 6х + Зу - 4z -12…

A: the point at which the line meets the plane is (x,y,z) = (2,-207,277)explanation is given in below…

Q: Prove that the planes determined by the equations ax + by + c z = d and αx + β y + γ z = δ are…

A: Given planes, ax + by + c z = d αx + β y + γ z = δ

Q: Given the planes π1 : x − 2y + 3z + 1 = 0 and π2 : 2x + y + z + 2 = 0. Find the equation of the…

A:

Q: Which of the following points is on the xy and yz planes, but is not on the xz plane? a) (2, 0, 0)…

A: We can represent 3D coordinate system.

Q: Are the following planes parallel or perpendicular or none? 3r+2y-5z – 9 = 0, 3x– y+2z – 9 = 0

A: Consider the given plane. The general for of the plane is defined as, A1x+B1y+C1=DAnd,A2x+B2y+C2=D…

Q: If 1x, y2 are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

A: If (x,y) are the coordinates of a point P in the xy-plane, then x is called the _________  of P and…

Q: The plane containing the point (2,5,0) and parallel to the plane 3x – 7y + 6z = 8 has equation Ах +…

A: Recall:      The equation of the plane parallel to Ax+By+Cz=D and passes through the point  α,β,γ ,…

Q: 0- Draw a sketch of the Plane of 4x-tyt22-9=0

A: Solution

Q: Find the point of the intersection of the plane P: 2x - 3y + 4z + 14 = 0 and the line L:r = 1 – t,…

A: Given the equation of line and plane  2x−3y+4z+14=0x=1−ty=1+tz=2+3t

Q: Determine whether or not the planes f1:   3x  –  y  + z – 2 =  0 f2:     x + 2y –  z + 1 =  0 f3:…

A:

Q: Find the point Q symmetric to the point P (1; 3; —4) with respect to the plane 3x+y-2z=0

A:

Q: Find the point on the plane x+ 2y - z 12 that is nearest the origin.

A:

Q: Find the distance between the planes M: 3x – 4y + z – 17 = 0 and N: 6x – 8y + 2z + 68 = 0.

A:

Q: find the trace of the plane in the given coordinate plane.  3x + 4z = −2, xy

A: To find the trace of the plane in the given coordinate plane  3x+4z=-2 --- (1) in the xy plane

Q: Which of the following planes contains the z-axis?(a) z = 1 (b) x + y = 1 (c) x + y = 0

A: In 3 dimensions, the rectangular coordinate system has 3 perpendicular axes, x, y, and z. Any point…

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

A:

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1=0 3x+3y+3z+1=0…

A: True

Q: The line L(t) = (4 – 3t, 3, 1 +t) intersects the plane 3x – 3y + 2z = -16 at the point when t =

A: To find the point of intersection of the line and the plane, substitute the values of x,y, z from…

Q: Зу — 2z 3D 6

A: Use a graphing utility to plot the plane, 3y-2z=6 .

Q: Find the value of k for which the planes: 2x-ky+4z=1 and kx+y-3z%3D2 are orthogonal.

A: we have to find the value of k for which the planes 2x-ky+4z=1 and kx+y-3z=2 are orthogonal.

Q: The diagram approximately illustrates how the planes intersect. x+y+z+1=0 2x+2y+2z+1= 0 2x+2y+2z+2=…

A: We have to solve given problem: Concept:

Q: 2) Find the equation of the plane that is orthogonal to the planes 3x-2y-2z=1 and x-3y-10z = 4 and…

A: Given: The equation of two planes 3x-2y-2z=1 and x-3y-10z=4 and the equation of one line…

Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 12у — 9г — 3 %3D 0 (a)…

A:

Q: ) Find the equation of the plane passes through the point P(2, 2, 3) and perpendicular to the two…

A: To find the equation of the plane that passes through the point P (2, 2, 3) and perpendicular to the…

Q: Find the common point(s) of the planes given by II : II2 : Il : 3x + 2y – 4z = 18 y+ z= 3 Зд — 2у —…

A:

Q: Find the equation of the plane which passes through O and is parallel to z –- 3x = -2 %3D х+ y + z =

A:

Q: Find an equation for the plane that passes through the point (1, 2, 3) parallel to u = 2i + 3j + k…

A: Given:u = 2i + 3j + k and v = i - j + 2kFirst find cross product

Q: Find the point on the plane 3x + 2y + z = 6 that is nearest the origin.

A:

Q: Determine whether the planes are parallel, perpendicular, or neither. Зх — 18у — 15г - 2 %3D 0 (a)…

A: Given:   Equations is given

Q: Determine whether the planes are parallel, perpendicular, or neither. 2x – 10y – 8z – 1 = 0 (a) | -x…

A: Given problem:- Determine whether the planes are parallel, perpendicular, or neither.   (a) 2x…

Q: Find the point at which the line intersects the given plane. x = 3 - 3t, y = 4t, z = 1 + t; x + 2y -…

A: Given line ,x=3-3ty=4tz=1+t   -1and plane , x+2y-z=6

Q: H.W 8- Find equations of the planes that are parallel to the plane x +2y- 2z= 1 and two units away…

A:

Q: If the line L: X = 3 + 2t , Y= 2t , Z = t intersects the plane X+ 3y - Z =-4 in a point P. The…

A:

Q: Find the point of intersection between the planes TT :x+y-z =1, n, : 2x – 3y -9z = 10 and n, : x +…

A: The three planes are, π1=x+y-z=1 π2=2x-3y-9z=10 π3=x+2y-3z=-4

Types of Bias

Statistics is the study of data collection, organization, analysis, interpretation, and presentation. Statistical bias is a characteristic of a statistical technique or its findings in which the expected value deviates from the actual root quantitative parameter being estimated. According to the actual definition of bias, it refers to the tendency of a statistic to overestimate or underestimate a parameter.