Find the general equation f the plane passing through P(-!,3,-2) and having n(-2,1,-1) hormal. O so

Q: 2- We can write the vector x = (19,–1,–) in R³ as a linear %3D combination of the vectors x1 = (4,2,…

A:

Q: 7. Let ui (1,4, 2), из (0, 3, 1), из — (1,1, 1), ид — (1, 3, —3) represent four 6. points in the…

A: Since part (i) is very lengthy, we solve first part only. For other part please resubmit.

Q: Show that except in degen-erate cases, (u * v) * w lies in the plane of u and v, whereas u * (v * w)…

A: Show that except in degenerate cases, (u x v) x w lies in the plane of u and v, whereas u x (v x w)…

Q: in 4 method ТВС- тво-1 Example 1.8.6 Find the p sic equations of the plane that passes through the…

A:

Q: Compute the orthogonal projection of 7 = proj,(v) = 4 [1] onto the line L through -4 and the origin.

A: Given:    Data is given

Q: Compute the orthogonal projection of 7 = projz (7) = onto the line L through and the origin.

A: The given data is: v→=-69 To compute the orthogonal projection of v→=-69 onto the line L through -76…

Q: Compute the orthogonal  projection of v = [ -3, -3 ] onto the line L through [ 2, -2 ] and the…

A:

Q: The scalar  equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is:   a.…

A:

Q: The scalar equation of the plane passes through (-1, 3, -2), (-1, 2, -1) and (4, 1, -2) is: 2x + 5y…

A: Put the points one by one on the given planes and check satisfied or not

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Compute the orthogonal projection of i -5 onto the line L through -4 and the origin. proj, (5) =

A: Here we use for product to find he projection.

Q: What is the scalar projection of á = (1,0, 1) onto b = (0, 3, 4)?

A:

Q: FBShow that the vectors (taken from a vector consisting of all functions of the real numbers) are…

A: The objective is to show that the vectors are linearly independent.

Q: Determine the set of points satisfying the condition described by Iz – 2i| + |z + 4i| express in the…

A:

Q: Determine the Eq.  of plane (M) pass through points A(0,2,0), B(1,1,1), C(-1,0,2)

A:

Q: A normal vector to the graph of z = r²y at the point (2, 1, 4) is Select one: (4, 4, 1) О -4, -4, 1)…

A:

Q: 1 Compute the orthogonal projection of v = onto the line L through -6 and the origin. 2 projz (7) 2.

A:

Q: 20) Find the equation for the plane in 3-space passing through the points (2,3,2), (0, -4, 3) and…

A:

Q: The equation of the plane passing through A(2,1, – 1), B (0, –2,0), and C(1,-1,2) is: O 2x+y-z=0…

A: solve the following

Q: 3. Show that the vectors v₁ = (0, 3, 1, -1); v₂ (6, 0, 5, 1); v =(4, -7, 1, 3) form a linearly…

A:

Q: 7. Find the equation of the plane passing through the points (1, 1, 2), (3, –1,6) and (5, 2,0).

A: To find the equation of the plane passing through the given points

Q: The vectors in Z22 are [ O, O] , [ O, l], [l, O ], and [l, l ]. (How many vectors doesZn 2 contain,…

A:

Q: Compute the orthogonal projection of = 3 onto the line L through -2 and the origin 2 proj, (v) =

A:

Q: Show that the vectors v, = (0, 3, 1, -1); vz = (6, 0, 5, 1); vz = (4. –7, 1, 3) form linearly…

A: Solve the given problem.

Q: The plane through the points (1, 2, 3), (1, – 1, 1), and (–1, 1, 1). |

A:

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: 8. Find the scalar equation of the line passing through the point (1, 5) that has a normal vector…

A:

Q: Find the moment vector m and m of p = [2,3,0] about Q: (2, 1, 0) acting on a line through A: (0, 3,…

A:

Q: Find the scalar equation for the plane passing through the points P-(-1. 5.-1. P=(-1, 6, 5), and…

A:

Q: A point moves so that sum of the squares of its distances from the vertices of a triangle is always…

A:

Q: Find basis for the set of vectors in R2on the line y=nx. where n is last digit of your arid number.…

A:

Q: 7. For the vector ū = (1,2,3), compute the 1-norm, the 2-norm, and the 0-norm.

A:

Q: Find the equations of the tanget plane and normal line to the graph of In(2?)x-을=3y3-VE at the point…

A: Equation of tangent plane f(x, y, z) = k at x0, y0, z0 is, fxx0, y0, z0x-x0+fyx0, y0, z0y-y0+fzx0,…

Q: 1 Defined in P,(R), p(x)=1,q(x)=x- and h(x) =x² -: -x+- 6. Investigate whether the vectors are…

A:

Q: 9. Find an equation for the plane containing the points (3,1, 4), (–1, –1,-1), and (0,2,2).

A:

Q: What is the maximum of || Ar||∞ if ||r||∞ = 1? What is the maximum of ||Ar||2 if |-|2 = 1? For…

A: A=2123 (a) We know that Ax∞≤max∑ka1k,∑ka1k,…∑ka1k when x∞=1. Ax∞≤max2+1,2+3=5 The maximum of Ax∞ is…

Q: (9) Find a vector parameterizat1on of the line r(t) which passes through the points P = (2, –6, 4)…

A: The given points are P=(2,-6,4) and Q=(3,5,-3). We have to do vector parametrization. We subtract…

Q: 8. Determine if point A(-1, -3, 9) lies on the plane T: 8x-3y+2z=4

A: The point lies on the plane if the coordinates of the point satisfy the equation of the plane.

Q: Find an equation of the plane containing the point P(2,1, –1) and having the normal vector N = -î+3…

A:

Q: 5 Find the equation of the plane passing through the points A(1, 2, –3), В(2, 1, 4), С(3,0, 1).

A:

Q: Find a nonzero vector orthogonal to the plane through P(2,5, 1), Q(-3, 1, –2) and R(5, –3, –1).

A:

Q: Compute the orthogonal projection of i = 1 onto the line L through 4 and the origin. projz (5) =

A: Vector projection

Q: Find the equation of a plane passes through (1, 2, 3), (3,2,1) and (-1, -2, 2) ○ 4x - 3y + 4z = 10…

A: This question is based on finding equation of plane that passes through 3 points.

Q: 5) An equation of the of the plane passing through the points P(0,2,1), Q(2,1,2), and R(3,3,1).

A:

Q: Find the particular number of orthogonal transectories of x2+cy2=1 passing through the point (2,1)

A: Given equation is x2+cy2=1........1. We have to find the particular number of orthogonal…

Q: Find a basis for the set of vectors in R^3 in the plane 3x - 2y + z = 0. Also state the dimension.

A:

Q: Usually there will be exactly one hyperplane in Rn that contains the n given points x = 0, a1, ... ,…

A:

Q: Sketch planeglven by Iz-31 = 1Z + lomplen the Cunve in the |ス-3| - |N+3i| 2. 2. 2. =フナ

A:

Q: 3. Find an equation of the plane passing through the points P = (5,1,1), Q = (1,1,2), R = (2,1,1)

A:

Q: Find a nonzero vector orthogonal to the plane through P(2, 5, 1), Q(-3, 1, – 2) and R(5, –3, –1).

A: