Three points A, B,C in R are given: A = (1,2, 3). B = (2,2, -1). C= (3,1,0). Find the coordinates of the point D lying on the line passing through A and B such that the vector CDis orthogonal to the vector AB.

Q: Find the vector v with the given length and the same direction as u.||v|| = 4, u = (−1, 1)

A: To find a vector v with the given magnitude of ||v|| = 4 and in the same direction as u = (−1, 1).

Q: Find two vectors that are orthogonal to the plane containing the points P = (4,-2,1) and R =…

A: We find two vectors that are orthogonal to the plane containing the points P = (3,0,1), Q =(4,-2,1)…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Introduction: The coordinate of a point x,y,z is actually the components of the position vector…

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Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: Given the vectors u = (2, -2, 3) and v = (-3, 2, – 1), calculate the vector projection of u onto v…

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Q: Find the unit vector orthogonal to the plane through the points P ( 12, 3, -4 ), Q (-1, -2, 2), and…

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Q: A vector u is a positive multiple of . Vector v = with a , what will be the signs of d, e, and f?…

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Q: Find a vector V that is perpendicular to the plane through the points A=(0,3,4) , B=(3,-5,−5) , and…

A: Find the vector AB and vector BC. The cross product of AB→ and BC→ gives a vector which is…

Q: Given A = x(2z -y) + ŷ(3x-2z) – 2(x+3y), find a unit vector parallel to A at point P =(-2, 1,–3).…

A: Vector valued functions are the rule that used to fix or associate a vector to a particular point…

Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

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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 a unit vector perpendicular to plane PQR determined by the points P(-3, 3, -4), Q(4, -1, - 23),…

A: Given query is to find unit vector perpendicular to PQR.

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 a unit vector perpendicular to the plane of P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

A: Given P(1, -1, 0), Q(2, 1, -1), and R(-1, 1, 2) .

Q: Find a unit vector that is orthogonal to both u and v. u = (-8, -6, 4) v = (17, -18, -1)

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Q: For the points A(1, 5, -7) and B(3, 0, 1) vector AB has coordinates

A: Given point A and B. Find vector AB.

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A: Explanation of the answer is as follows

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Q: Let A, B,C be three points not lying on the same straight line. a. Which set of points P is…

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Q: Consider the points below. Р(0, - 2, 0), Q(5, 1, -2), R(6, 3, 1) (a) Find a nonzero vector…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Given that L is a line in 2-space or 3-space that passes through the points A and B then the…

Q: If the vectors b, c, d are not coplanar, then can we say that the vector (ā×b)×(ē×d) + (ā×ē) × (dxb)…

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Q: Given points P = (2,1,5), Q = (-1,3,4), R = (3,0,6), af Find the unit vector orthogonat…

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Q: Find a vector ī that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4, –2),…

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Q: a. Find a unit vector perpendicular to the plane of P (4,2,1), Q (1,2,0), R (1,1,2). Whereas P is a…

A: Due to Bartleby guidelines, only 1question can be solved. Please repost the remaining questions to…

Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( 5 , −…

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0) Which axis on…

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Q: Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the…

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Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find the position vector for the vector v, whose initial point is (0, −2) and terminal point is (5,…

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (0, 1, 3, -1) V…

A: In  the given problem we have to find the vector v with the given length and the same direction as…

Q: Let P(4, - 3) and Q(- 1,2) be the initial point and terminal point, respectively, of vector V. Find…

A: Solution  Find position vector

Q: Given that a = (-10,9,13) and b = (14,–6,12), а. i) ii) compute the dot product. find a vector…

A: (i) Given  a→=-10i→+9j→+13k→b→=-14i→-6j→+12k→ Then,  a→.b→=-10i→+9j→+13k→.-14i→-6j→+12k→…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

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Q: Find the vector v, where u = (-1, 3) and w = :(-3, -1). v = u + 2w Illustrate the specified vector…

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Q: Find the vector joining the points P1= (-3, 1) and P2= (5, 2) %3D %3D in terms of i and j.

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = ( – 1,…

A: find the explanation below

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

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Q: What value(s) of a are necessary for vectors i = (2, a), and w = (4a, 3) to span R?

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Q: Find a vector, in component form, that is orthogonal to the plane containing the points P = (5, 2,…

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Q: Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis on…

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Q: Find the vector v with the given length and the same direction as u. ||v|| = 3, u = (1, 0, 1, –4)

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Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

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Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector <a, b, c> is: ax+by+cz+d=0 Therefore,…

Q: (a) Find a vector perpendicular to the plane that contains the points P(1, 0, 0), 0(2, 0, – 1), and…

A: It is given that the plane contains  P(1,0,0), Q(2,0,-1) and R(1,4,3). Let, Equation of plane…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Let us consider a line l joining by  two points A  and B. Consider a point P (not on line l ) then…

Q: Find a vector, v, in component form, that is orthogonal to the plane containing the points P = ( –…

A: Topic = Vector