O Find the distonce from the point pC1,\, 1) to the plane 2K-3y+72=1

Q: which of the toihts PC6,L3), Q (-5,-1,4), and R(0,3,8)15 c losest to the X2-Plane? which paint lies…

A: A point in 3D has (x,y,z) coordinates. A point on XY plane has (x,y,0) coordinates i.e. z=0 A point…

Q: What is the distance of the origin to the plane through (√3, √3,0), (√3,0, √3) and (0,√3,√3).

A: We have to find the distance of the origin to the plane passing through  and .

Q: 7. a) Find the equation of the plane passes through the point P(1,2,-1), perpendicular to…

A: We have to solve given problems:

Q: (0,1,1) to the line of intersection of the planes : x + 2y + z = 1 x - y + 2z = -8

A:

Q: State the equstion of the yz plane

A: We have to find equation of yz plane

Q: Find a plane through P (2, 1, 1) and perpendicular to the line of intersec- tion of the planes:…

A: find a plane through P2,1,1 and perpendicular to the line of intersection of the planes  2x+y-z=3 ,…

Q: Let 5x + 3y + 10% = 0 be the equation of the 3 plane in R³ spanned by (1, a, 0) and (1,0, b). Find…

A:

Q: 19. Find the Cartesian equation of the plane a) passes through point A(6,- 7, 4) and parallel to the…

A: To find the Cartesian equation of the plane, a)Which passes through the point A6,-7,4 and parallel…

Q: ind the equation of the tongent plane to fox,y)=x²-2xy + 2y ² slope 2 in the positive x direction…

A:

Q: Q1-)A-) Find the distance from the point (0 ,1,1) to the line of intersection of the planes : x + 2y…

A: Use equation of plane

Q: Suppose P is the plane described by the equation ax+-by + cz + d = 0. Given two points (X0, Y0, Z0)…

A: Given equation of plane ax+by+cz+d=0. The plane ax+by+cz+d=0 will divide the xyz space into two…

Q: Suppose the solution set of x1 + x2+2x4 What are the equations of the plane at (1,2,3,4) which is…

A: First we find direction vectors of the plane of solutions.

Q: ) fnd the equ. f Plane that Contains the two line S: X-1=3+ 6=そ X-リ=Z-4 and Passes through origin?…

A: Given problem:- find the equation of Plane that contains the two lines x - 1 = y + 6 = z ,    x= y =…

Q: Find the distance from the point (1,1,1) to the plane 2x+2y+z=0

A: Solution :-

Q: The equanon of the plane passing through the line of intersection of the planes. Find 3x +y-52 +7 =…

A: We have to find the equation of the plane passing  through the intersection of the planes…

Q: Fud the Line pussing through the posnt (!,-l,o) and purrllel to the Eme of intersection of planes (X…

A:

Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.