Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u = (-1, –2, 3) and i = (3, –8, –9). 7(t) = with -o < t < ∞

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

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

Q: Find an equation of the plane that passes through the point P(2, 5, 1) and has the vector n = (1,4,…

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Q: 7. Find an initial point P of a nonzero vector u = PQ with ter- minal point Q(3, 0, –5) and such…

A: We have to find an initial point P of a non zero vector u = PQ→,  with terminal point Q(3, 0, -5)…

Q: Find a non-zero vector 7 perpendicular to the vector u 12 [3]. -6

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Q: * Find the values for h for which the vectors are linearly dependent: 7

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Q: P that is orthogonal to the vector AB. . B e distance from the point P(-3,1,9) В(-2,3, —4).

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Q: Express the vector t as a linear combination of the vectors u, v and w: t = (5,30, –21), u = (5,2,…

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Q: 4. Find the vector v that is orthogonal tou=i+j+k and whose r-component and z-component are 2 and…

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Q: EX/ Find The normal vector to A = 2i-3j+4K, B =i-2j+ 5K %3D ĀxB =Ñ =1? ĀXB=N -3 4 = -7i-6j-K %3D - 2…

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Q: Find a non-zero vector v perpendicular to the vector u = [ -1 ]                          [ 8 ]

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Q: Find the terminal point of a vector v = with an initial point P(0, 6, 2).

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Q: Find the initial point A of the vector that is equivalent to (3,7), and whose terminal point is…

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Q: Determine the shortest distance from the point (3, 4, 5) to the line through the origin parallel to…

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

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Q: Find the values of x, y and z that satisfy the vector equation 1 3 ·A·B·0-0-0-0 x 3 +y -2 +2 1 = 1…

A: We want to find values of x, y and z which satisfy given equation.

Q: Q2) A- Use two methods to create the vector x having 100 regularly spaced values starting at 5 and…

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Q: The position vector of a moving particle in space at time t is given by the vector function r (t) =…

A: position vector of particle in space r→(t)=12(5-t)2i→+(2t-1)j→+43(5-t)32k→

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

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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: 1. The vector in the opposite direction to u = = (-1,0) and of half its length is

A: Explanation: Given that,  Vector u=-1,0 find the length of this vector  length of vector u =…

Q: Find the value of t such that the vectors v=(2t+1,-3,3t-2) and w=(7,4t+2,2) are orthogonal.

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Q: Find a vector equation for the line segment connecting the points P = (-9,–6, 8) and Q = (-15,…

A: We have to find a vector equation for the line segment connecting the points P=-9,-6,8 and…

Q: 2.) Find two vectors that are orthogonal to the vector v = 8i - j

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

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Q: M contains the point with coordinates (0,0,1) 2 M is orthogonal to the vector 0

A: Introduction: The general equation of Plane is ax-x1+by-y1+cz-z1=0

Q: If the vector K az+Lay+ Ma, shows the maximum increase rate and direction of the scalar V at point…

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Q: The z-coordinate of the terminal point of the vector v=-5i-19k whose initial point is (-1,-4,-5) is

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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/…

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

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Q: The orthogonal projection of the vector v =3i-j+k on the vector b 2i-j+k is

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Q: Q2: Determined the component of the vectors at each point…

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Q: 4. A vector normal to the paraboloid z = (x² + y*)/2 is (a) (х, у.1). (b) (2x,2y,–1). (e) (-х,-у.1).

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Q: 4

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Q: what are the components of a vector? what if the initial point is not (0,0)? given a vector v and a…

A: A scalar is a real number. A scaler is a single, independent number.  A vector is a ordered…

Q: If the vector v has initial point P, what is its terminal point? v = (0, 0, 3), P(0, 3, -3) (x, y,…

A: Let's find.

Q: Find a vector perpendicular to the graph of z = - 3 x2 + 9 y2 – 7 x y at the point (8, 2, -268).

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

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Q: Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

A: Given: Let A(7,6,2) and B(2,14,2) be the two points the line passes through To find: vector equation…

Q: (2t, 1 – t, 4t) is a parametrization of the line passing through the point (0, 1,0) and also…

A: The statement : &lt;2t, 1-t, 4t&gt; is a parametrization of the line passing through the point (0,…

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

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Q: ) Find a vector equation for the line that goes through the points (7, 6, 2) and (2, 14, 2). F(t) =…

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

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Q: If two objects travel through space along two different curves, it's often important to know whether…

A: To solve this we must figure out at what t's positions are equal for each vector component. so, set…

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: Find the values of x, y and z that satisfy the vector equation 1 3 ·¤-A-D-A-A-D 3 +y-2 +2 1 1-2 +3…

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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,…

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

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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.