Find a vector equation for the line through the point (-3, –1, 8) perpendicular to the vectors ū = (8,4, 8) and v = (-3,5, –8). F(t) = | with -o

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

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

A: We have, Equation of plane through P0 =(x0, y0, z0) with normal vector n = <a, b, c> Vector…

Q: Find the domain of the vector function 7(t) = (v4 – t², e-3t, ln(t + 1)

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Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Let DE be the vector with initial point D(8, 6) and terminal point E(-1, 5). Write DE as a linear…

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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: Let v be the vector from initial point P1 = (-1, 3) to terminal point P2 = (2, 7). Write v in terms…

A: Given : the two points are given as P1=-1,3 and P2=2,7 To find: a vector v from initial point P1 to…

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

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Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: Find the point A (a, a, 0) on the line y = x in the xy-plane, such that the vector AB is…

A: Solution is given below:

Q: Let v be the vector from initial point P1 = (-3, 4) to terminal point P2 = (6, 4). Write v in terms…

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Q: Consider the points P(3, x, -2) and Q(5, 3, 4) in R3 . Find x so that the vector from P to Q is…

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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: Find an equation of the plane that passes through the point P(4, 6, 3) and has the vector n = (1,6,…

A: I have stated the used formula in the solution.

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: Prove that the vector T′(t) is 0 for an object moving in a straight line.

A: Here an object moving in a straight line. The path of the object can be given as follows.…

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: 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: Determine all vectors v that are orthogonal to u. (Set v, = t and v3 = s and solve for v2 in terms…

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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: Find basis for the set of vectors in R'on the line y = nx. Where n=9.

A: Note that ℝ2 forms a vector space over the field of Real numbers ℝ. Let W =x1x2∈ℝ2  : x2 =9 x1 ,…

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: 3. For the vectors b= (2, -1, -2) and a = (0, 4, –3) (a) Compute the projection of vector b onto the…

A: Consider the equation

Q: Find a vector v that is perpendicular to the plane containing 3 -() 6 and 0 2

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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: Find the coordinate vector of p = 2 – 4x relative to the basis B = {q,,q,} for P1 where q1 = 3 + 8x,…

A: Given : We are given a vector,  p = 2-4x  and a basis  B = q1, q2,                 where,  q1= 3+8x…

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

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Q: (c) Find the vector equation of the line of intersection of the planes x-2y+z=0 and x+y=z= 1.

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Q: Let v be the vector from initial point P1 = (-4, -4) to terminal point P2 = (6, 2). Write v in terms…

A: Given initial point P1=-4,-4 and terminal point P2=6,2. Given points can be written as: P1=-4i-4j…

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

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Q: Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n = 9i + 2j…

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Q: Let u=(-2, 0, 1) and v-(-7, -1, 3). Find the value of the j-component in the vector 5u-6v

A: The given vectors are:u=-2,0,1 and v=-7,-1,3First we find the vectors 5u and 6v.

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 a vector equation with parameter t for the line of intersection of the planes x + y + z = 4 and…

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Q: Find the value of h for which the vectors are linearly dependent

A: The given vectors are 1-14 , 3-57 , -15h The vector v3 are linearly dependent if the equation…

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…

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Q: 5. Find the vector equation of the line passing through A(4, -3) that is perpendicular to x - 3y + 6…

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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: Let v be the vector from initial point P1 = (-4, -4),to terminal point P2 = (6, 2). Write v in terms…

A: Initial point is P1=-4, -4 & terminal point is P2=6, 2.

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: For which value of x do the following vectors form a linearly dependent set in R V =| x, x,

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Q: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

A: Find a nonzero vector u with initial point P(2,-3,6) such that: (a) u has the same direction as v =…

Q: Find a non-zero vector 7 perpendicular to the vector u = 5= [8]. 6

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Q: Find basis for the set of vectors in R2 on the line y= nx . where n=9.

A: Explanation of the solution is given below...

Q: Show that the vectors (x1, Y1) and (x, 2) in V, (F) are linearly dependent if

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Q: Q3) Find the vector ž, which is perpendicular to vectors ã = (2,3, –1) and b = (1,–2,3) and…

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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: 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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Contingency Table

A contingency table can be defined as the visual representation of the relationship between two or more categorical variables that can be evaluated and registered. It is a categorical version of the scatterplot, which is used to investigate the linear relationship between two variables. A contingency table is indeed a type of frequency distribution table that displays two variables at the same time.

Binomial Distribution

Binomial is an algebraic expression of the sum or the difference of two terms. Before knowing about binomial distribution, we must know about the binomial theorem.