Position vector We can identify a point with the vector that runs from the origin to the point. This is called the position vector. In the plane, the vector from the origin to a point (x, y) is \tmmathbfr = r\tmmathbfi + y\tmmathbfj The position vector in three dimensions is \tmmathbfr = \tmmathbfi + y\tmmathbfj+ z\tmmathbfk Problem For example, if a particle travels around the unit circle in the counter-clockwise direction in a time 27 the position would be given by \tmmathbfr(t) (t)\tmmathbfi+ (t)\tmmathbfj 0

Q: he points A(1,-2,4) and B(2,-4,1) cach make direction vectors with the point (Xo.Yo, Zo). The point…

A: The Parametric equations of the line are the components of the vector equation , and have the form…

Q: Q3) If P(2,-2, 1) , Q(3,-1,2) and R( 3,-1,1) ノ の)ind the area of the triangle determined by the…

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Q: Bluetop Cab charges $3.20 for the first mile and$1.35 for each additional mile or part of a mile.

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Q: 1) Find the vector and parametric equation of the line in R³ through the point P = (1, 2,-4) 5…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: use vectors

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Q: Let(vector u)=(-2,-3), (vector v=(-3,-5) and vector w=(-2,-3). Find the vector x that satisfies…

A: u=(-2,-3)v=(-3,-5)w=(-2,-3)Calculating x:

Q: 4) Consider the vectors u = [3, -2] and v= [-5, 4], write a = [-24,18] as a linear combination of u…

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Q: Find the projection of = 5 2 -7 onto the line I with vector equation = td where d = -5 -3 6

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Q: A = [-2,4,-2,-4,        2,-6,-3,1,        -3,8,2,-3,        0,2,5,3]  Find a non-zero vector R^4…

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Q: 5. In each case, find the equation of the line with the given properties. (a) Passing through the…

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Q: Let vector a = and vector b= find the projection of vector b onto vector a

A: Please see the below picture for detailed solution.

Q: O a. X=4+ 7^, Y= 7+ 1\, Z= 10+6A

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Q: vector a=(8,-3) vector b=(2,4) what is the angle theata between vector a and b tail to tail what is…

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Q: The cross product of vectors a = (-1, 4, 6) and b = (3, 0, -2) is %3D

A: The cross product of vectors is given below

Q: Prove using vectors that the points represent the vertices of a triangle then (1) Find the area of…

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