) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) = || with -o

Q: 9

A: We need to determine all the values of the constant a for which the vectors

Q: The vector z = (2 + 2i) ( -V3 + i) lies in * the

A: The vector equation is z=2+2i-13+i.

Q: Assume that 0 < a < 1 and 0 < b < 1. Find the stable vector of P 1 - b ]

A: Let w= [x y ] is a stable vector of the given matrix.  So, the equations to solve are:

Q: 1 Suppose a line passes through the point (1, 1 and parallel to the 2' 3 plane x + y + z = 0. Then…

A: The direction vector of the normal to the plane is (1,1,1) Given that the line is parallel to the…

Q: Find a vector equation with parameter t for the line through the points (–1, –7, –4) and (-9, 8, 2).

A: we know that vector equation of line which passes through pointsx1,y1,z1,x2,y2,z2 is given by…

Q: 2. The plane containing the point P(Xg» Yor Zo) and having the normal vector n = (a, b, c) is…

A: Equation of a plane passing through the point Px0, y0, z0 and perpendicular to the vector n=a, b, c…

Q: 8. Let C = 2 c=(; 1) - (;) ()- and b = Find a 2-vector z such that Cz = b.

A: we have  C=112-1b=11   we have to find a 2-vector such that  Cz=b

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v = ai+bj, where a and b…

A: It is given that initial point of vector v is (0,0). The objective is to write vector v in the form…

Q: 2v in Given vector U= (2,5) and v = (1, –3) , determine the value of u component form.

A: Topic:- vector algebra

Q: 4. Define the function T: R² → R as 1 T(v) = Av = |-2 4 V2 %3D -2 a. Find T(2, 4). b. Find the…

A: We need to find pre image.

Q: Find a vector function that represents the curve of intersection of two surfaces: z = x² - y? and x²…

A: Idea  1) Solve the equation in term of only one variable (2) assume in term of parametric function…

Q: 2 1 3. Show that that the vector u = |-5| is a linear combination of the vectors v1 = |-3 3 2 2 V2 :…

A: The given vectors are: u=2-53, v1=1-32, v2=2-4-1  and  v3=1-57 Vector u=2-53 is a linear combination…

Q: (9) Show that the space curve given by the vector equation r(t) = passes through the point (1, 4,0)…

A: Explained below

Q: 3- The scalar component of the vector F in the direction of K is (K.F А- .K, В- K C-

A:

Q: 6. Find the distance of the point (-1,1) to the line given in vector form (x, y) = (2,0) +t(4, 3).

A: Given that: The point is (-1, 1).The vector is:  (x, y)=(2, 0)+t(4, 3)

Q: 2. Find the magnitude of the vector PQ whose initial point is P(1, 2) and end point is at Q(4, 3).

A:

Q: 4. Determine whether the given vectors form a fundamental set on the interval (-0, 00). -()-. X1 =…

A:

Q: 3) Write down the equation of line in a vector parametric form, scalar parametric form and standard…

A:

Q: Let x=⟨1,1,1⟩ and y=⟨0,3,−2⟩Find a unit vector that is orthogonal to both x and y

A: If w is an unit vector which is orthogonal to x and y, so

Q: Q1. If O (0,0,0) in (x,y,z) 3-D space and r(2,5,1) draw the vector in 3D and find its direction.

A: Plot point in 3D

Q: Show that the vector form (x, y, z) = (-5, 1,0) + t(3,2, 1) for some parameter t ER satisfies the…

A:

Q: Find all values of the scalar k for which th e two vectors are orthogonal.

A:

Q: -11 and ỹ = Express the vector u as a linear combination of x 28 x+ y.

A:

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

A:

Q: 2 3. Show that that the vector u = -5 is a linear combination of the vectors v1 3 2 ------ 2 U2 = -4…

A:

Q: - a) Determine the vector equation of the line of intersection of these 2 (1) x + 2y + 2z = -3 (2 2x…

A: Note:  part(b) is the independent subpart of part(a) and also it is incomplete. so part (b) can't be…

Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

A: Given, Normal,n=(2,-4,1) Point, P=13,23,1     Find the equation of the plane with normal vector n…

Q: X/ Find The normal vector to A = 2i-3j+4K , B = i-2 j+ 5K AxB=Ñ =? ĀXB=N -3 4 = -7i-6j-K %3D - 2 Hw/…

A:

Q: Which of the following is the equation of the plane passing through the point (0,2,-3) and with…

A:

Q: The vector v with initial point (0, 0) is shown below. Write v in the form v = ai+bj, where a and b…

A:

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

A:

Q: Let A = (0, 0, 0) and vector v = (-3, 0, 1). Find vector equation of the line containing the point A…

A: Given point on the line is A=(0,0,0) and the line is parallel to the vector V=(-3,0,1)

Q: -) Find the vector form F(t) = ro + tu of the line through the points P(2, 7, 5) and Q(7,8, 12) Find…

A:

Q: 1. Show that the given vector functions are linearly independent (-00,00). on x; (t) =

A:

Q: 2 3. Show that that the vector u =|-5 is a linear combination of the vectors vi = -4 and vz = 3.

A:

Q: 3. (a) Find the terminal point of the vector that is equivalent to u = (2, 3) and whose initial…

A:

Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

A:

Q: Find a nonzero vector u with initial point P(-1, 3, -5) such that u has the same direction as v =…

A:

Q: (8) Find a vector parameterization of the line r(t) which passes through the point P = (1,2, –8)…

A:

Q: 1. Show that A(r - ro) + B(y - yo) =0 is an equation for the line in the ry-plane through the point…

A:

Q: 3. Find a vector equation of the line going through the point A(4, -5, 2) that is orthogonal to both…

A: The detailed solution is given in the next steps.

Q: 2 -a) Find a unit vector perpendicular to the plane that passes through the points P(1,4, 6), Q =…

A:

Q: 32. a) Determine the vector equation of the line of intersection of these 2 planes: x + 2y + 2z = -3…

A: According to Bartleby guidelines I can only answer the first question of the given two problems.

Q: Find an equation of the plane that passes through the point P(5, 6, 2) and has the vector n = (1,7,…

A:

Q: 1. Show that the vectors u̟ and uz parallel to lines L1 and L2 respectively, are orthogonal. L1: x =…

A: The given equations of lines are: L1:x=5-2t, y=-7+t, z=6+4t and L2:x=2+3t, y=5+2t, z=1+t Rewriting…

Q: Find the orthogonal projection of the vector b =-1 on Nul(A), where -2 -2 3 -10 A = 1 -1 2 3 1 -3 3…

A: For the solution follow the next steps.

Q: Suppose that u = (0, b) is a non-zero vector in R?. Show that the line L = Span({ủ}) has Cartesian…

A: Consider the given information.

Q: 2. Find the equation of plane which passes through the point (1,2, –3) and the vector i – 2j + 3k is…

A:

Q: 2. Determine the vector equation of the plane that contains the following two lines. L1: 7 = [ 4,…

A:

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.