1 Let C = [c1, c2, c3] = -1 2 3 -1 Find the point z in the plane spanned by cị and c3 closest to c2. What is the distance from z to c2?

Q: Let 6. 21 2 V2 = 4 9 For what value of h is y in the plane spanned by vj and v2? h =

A:

Q: Find the points where the liner(t) = 4 − 3t, 8 + 7t, 5 + t, −∞ < t < ∞,intersects each of the…

A: The point where the line intersects co-ordinate planes, one of the co-ordinates must be zero.

Q: Find the projection of d on the plane P if a 4 and P has the equation x + y+ z = 1.

A:

Q: If UV bisects XY at point W, which statements must be true? Select all the true statements. (A UW E…

A: Given that U̅̅V̅̅  bisects X̅̅Y̅̅at point W U̅̅V̅̅ bisects X̅̅Y̅̅ means U̅̅V̅̅ divide line XY in two…

Q: Let ABCD be a trapezoid with bases BC and AD. Let 0 = AB n DC be the point at which the lines…

A: Given that ABCD is a trapezoid with bases BC and AD, so BC and AD are parallel.…

Q: Which of the following planes contains the z-axis?x + y = 1

A:

Q: Suppose that O is the circumcentre of AABC and points X, Y, and Z are chosen so that BC, AC, and AB…

A:

Q: Vaughn Pang sketched trapezoid RUIZ on a coordinate plane. RUIZ has vertices located at R(1,4),…

A:

Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

A:

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

A:

Q: 1 2x 3y + z = 0 and 2 +t - 1 1

A:

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

A:

Q: The dimension of the set W = {(2t – s, s, t) : s, t e R} of R is equal to: %3D

A: The dimension of the set W={(2t-s,s,t) : s,t ∈ R} of R3 x=2t-s y=s z=t (t,s) ∈ R   This can be…

Q: Find the points on the cone z? = x² + y? that are closest to the point (3,2,0)

A:

Q: If EF is the perpendicular bisector of CD, find x.

A: Given,          EF¯ is the perpendicular bisector of CD¯ .

Q: ind a plane containing the point Gl,2,-3) and the line of intersection of the pladnes -X+3y -Z E -7…

A:

Q: Find the eguatien of the tangett line and nemat plane to the cune; Y. cest Ces(zt)i + st sinCet) j +…

A: Given r=cost cos2ti+cost sin2tj+sintk

Q: Use the diagram to name al of the points that are not coplanar with points Q. K, and L. N. M OK OM…

A: The two line in the 3D plane is are coplanar if the planes intersect each other or are parallel to…

Q: Find an eguaton for the set of all points (a sy, z) equiditant fom point (1,0,2) and

A:

Q: A. Use the figure on the right to name each of the following: 1. three collinear points 2. three…

A: A) 1) Collinear points are the points which are on the same line. Hence 3 collinear points are A , P…

Q: Evaluate x* zdS, where S is the part of the plane z = 1+4x + 3y above the rectangle [0, 3] x [0, 5]

A: Please see the below picture for detailed solution.

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: Evaluate O xy?dx + x5dy, where C is the rectangle with vertices (0,0), (6,0), (6,4), and (0,4)

A: Answer and explanation is given below...

Q: dA where R is the quadrilateral with the 5: Evaluate RI+y vertices (1,0), (4,0), (0,1), (0,4) using…

A: The solution are next step

Q: In AYZX, the midpoints of ZX and YX are M and N, respectively. The intersection of YM and ZN is G.…

A: M and N are the mid points of the side ZX¯ and YX¯, respectively. The measure of side YG is 22.

Q: If a = i+3j – k, b = 2i + 4j – 2k and c = -i + 2j +4k, find a number A such that d = a +b+ Xc is…

A:

Q: 1 7 Let a, 4 21 and b = 6. 1 2

A: here we can use matrix method to write the equation of plane and then we use the condition that b…

Q: The pole holding up one end of a volleyball net is perpendicular to the plane containing the points…

A: Paragraph proof: You are given that VW⊥WX and VW⊥WY,which implies that ∠VWX   and   ∠ VWY are right…

Q: Find the projections of the following onto the base planes of the given figures: i CF B ii DG A D C…

A:

Q: a Find the distance from the point pC,,1) to the plane 2K -3y+77=1

A:

Q: Find the coordinates of the point K that lies along the directed line segment from J(4,1) to L(8,11)…

A: As per our guideline we are allowed to do 1 question at a time. Please post other questions next…

Q: In ARST, SV bisects y ZRST. Find the coordinates of point T in terms of a. S (a, a) 2a T?, ?) V (2,…

A: Given that, Let ∠TSV=θ and ∠VSR=θ(∵SV is angle bisector)

Q: Given A ABC with points A (-1,2) B(4,-3) and C (0,0) dilated about a center at the origin by a scale…

A: The dilation factor is 3 Let the new coordinates be A'B'C' Then the new coordinates will be…

Q: If a? + b² + c² =1, then the distance from P (x0, y0, z0) to the plane ax + by + cz = 0 is |. |.…

A:

Q: Let ABCD be an isosceles trapezoid with AD = CD, and BD are 15, 18, and 10, respectively. Let K be…

A: Given an isosceles trapezoid ABCD with AD=BC and AB<CD. Distances from A to the lines BC,CD and…

Q: Show that w is in span(B) and find the coordinates of w with respect to B. B = 6.

A: Linear Algebra

Q: Let M be the midpoint of RQ and N bethe midpoint of OP. Use coordinategeometry to prove that ONQM is…

A: Given: Let M be the midpoint of RQ and N be the midpoint of OP. So, the figure is as follows:…

Q: Find a plane containing t and orthogonal to the pla

A:

Q: Which of the following represents a plane surfac whose x-, y-, and z-intercepts are a, b, and c…

A:

Q: Choose a set S of four distinct points in R3 such that aff S is the plane 2x1 + x2 – 3x3 12. Justify…

A:

Q: Find the points on the plane r - y = 2 – z closest to the point (1, 1, 1).

A: We will find the closest point on the given plane as following.

Q: E is the midpoint of Ad of a parallelogram ABCD.F is any point of diagonal BD such that 4DF=BD.EF if…

A: Given: 4DF=BD Construction: Draw the diagonal AC. It will intersect the diagonal BD at point H.

Q: Find the measures of 25 and Z4 in the given rhombus with the diagonals drawn. 4 19 m24 = degrees m25…

A:

Q: Given that A and B are parallel to the yz plane, that |A| = 2, |B| = 4, and A • B = 0, what can you…

A: Consider the provided question, Given A and B are parallel to the yz plane.

Q: Let h VI and y: 8 For what value(s) of h, is y in the plane generated by vị and v2?

A:

Q: In the given figure, AD is a median, and the length of BC is 18 units. What is the distance from…

A: Consider the given triangle ∆ABC with AB=15, BC=18 and AD is the median from the vertex A to the…

Q: Draw AABC and label the midpoints of AB, AC, and BC as X, Y, and Z. respectively. Let P be the…

A: We shall draw the triangle, along with all other lines in order to visualise the problem better…

Q: If p is the length of the perpendicular from the origin to the X y 1 1 line += 1, then prove that +…

A:

Q: Given Fxy 2) = (z², xy, yz) and C is a triangle in the plane x + y + z = 2 with vertices (1,1,0),…

A: We will use basic knowledge of vector calculus.

Q: E is the mid-point of side AD of a parallelogram ABCD. F is any point of diagonal BD such that 4DF =…

A: According to Given problem  Given E is midpoint of AD 4DF=BD To prove CG=DG