Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a magnitude of 5.|

Q: If v = 2i - 5j and w = i - j, find the vector projection of v onto w.

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Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: Find a nonzero vector orthogonal to the plane through points P(2,1,5), Q(-1,2,3), and R(0,3,3), and…

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Q: Suppose that u, v are vectors in R3 , u · v = 1, ||v|| = 1, the angle between u and v is π/3, and u…

A: The detailed solution is as follows below:

Q: Find an equation of the plane that passes through the point (1, 3, −7) and is perpendicular to the…

A: Direction ratio of the line n=j is (0,1,0)  Given that the line is perpendicular to the plane.  So…

Q: Find an equation of the plane that passes through the point (0, 0, 0) and is perpendicular to the…

A: The direction ratio of n = −3i + 2k is (-3,0,2) Given that that plane is perpendicular to n = −3i +…

Q: Find the B-coordinate vectors of ei and e2, where and B : %3D %3D %3|

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Q: 3. Given the vector ā = (x, y,=), where x = 0, y = 2 and z = 8 . Find the vector b with magnitude of…

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Q: If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at…

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Q: · Let 2 be the separation vector from a fixed point (x', y', z') to the point (x, y, z), and let z…

A: Since r is the separation vector from the point x',y',z' to the point x,y,z and the difference…

Q: If is a covariant vector in Cartesian coordinates x',x2.

A: In this question, we have covariant tensor (x1x2,x2x1) By using the transformation cartesian to…

Q: Let the vector ü = (k,5,-1) and v=(2k,k,3) are perpendicular in R, find the value of k that related…

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Q: Find vector V such that the vector has a length of 16 and makes an angle of n/3 with the x-axis.

A: Given problem:- Find vector V such that the vector has a length of 16 and makes an angle of π/3 with…

Q: Find the equation for the plane through the point Po = (2,3,8) and normal to the vector n= 3i + 8j +…

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Q: Find the equation of the plane passing through the point (3, 2, 2) perpendicular to the vector…

A: Given that the plane is perpendicular to the vector n=2i+3j-k. This means the direction ratio of the…

Q: Find vector u with the magnitude given that satisfies the given conditions. v (7, -1, 3), ||u || -…

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Q: Find the equation for the plane through the point Po = (3,4,3) and normal to the vector n=21 + 7j +…

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Q: O Find a unit vector (a vector with length 1) that has the direction of 3 2

A: Given below the detailed solution

Q: The plane contains the point (−2, 3, −1) and is normal to the vector 3i − 2j.

A: Given: point -2,3,-1   and vector 3i-2j

Q: Find a vector equation for the line segment from (2, -4, 5) to (6, 4, 4). (Use the parameter t.)…

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

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: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Given: f(x, y) = 3x² – 2y² at (-,0) in the direction from P(-,0) to Q(0,1). . What is the unit…

A: The given problem is to find unit vector of the function in which direction from point P(-3/4,0) to…

Q: Find the magnitude only for the vector from T(-2, 6, 1) to U(10, -3, -4).

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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 vector function that represents the plane that passes through thepoint p0 with position…

A: The plane passes through the point p0 whose position vector is r0→. The plane also passes through…

Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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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.

Q: Determine a unit vector in the direction in whichf(x,y) = 4x³ y² increases most rapidly at point…

A: Given that : - f(x,y)=4x3y2    at  P(-1,1) A function f(x,y) increases most rapidly at pointy P(a,b)…

Q: The plane through the origin that contains the vectors i - j and j - k

A: Given vectors are i - j and j - k. The plane is passing through given vectors i.e. 1i - 1j+0k and…

Q: Find the value of c that will make the vector 2 lie in the span of 0 2 and

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Q: Find the equation for the plane through the point Po = (5,4,6) and normal to the vector n= 2i + 3j +…

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Q: a) Find the vector that is parallel to the tanget to the circle x2 + y2 = 100 at the point (3,-4).…

A: a) Given equation of circle, x2 + y2 = 100. We have to find the vector equation which is parallel to…

Q: Prove that the vectors u = (cos θ, −sin θ) and v = (sin θ, cos θ) are orthogonal unit vectors for…

A: Given Data The first vector is u=(cos θ, -sin θ). The second vector is v=(sin θ, cos θ).   The…

Q: Find the coordinates of the point P on the line and a vector v parallel to the line x = 3t, y = 1 –…

A: Given parametric equation of line x=3t, y=1-t, z=3+5t

Q: Find a vector parametrization of line through P = (9, 8, 3) in the direction v = (4, -8, 6). %3D…

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Q: Find the vector equation of the line that is perpindicular to the line q(t) = (1,2, 3) + s(2, –1, 1)…

A: Consider a point P(1+2s, 2-s, 3+s) on the vector equation of the line. The vector joining points P…

Q: Find the vector W which is of length 6 and oppositely directed to u = (2,-2,1)

A: Given,          The vector w→ which is of length 6 and oppositely directed to u→=<2,-2,1>.

Q: If the magnitude of the vector u is √2 and its direction is 225°, then its components are:   (1,…

A: Solution of question as follows

Q: Given vector A = (1, -2, xy), it can be said that vector A is uniform vector.

A: A=(1,-2,xy)

Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: Find the coordinates of the point P on the line and a vector v parallel to the line. x = 8t, y = 5 -…

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Q: Let the vector ū = (k,5,–1) and v = (2k,k,3) are perpendicular in R', find the value of at related…

A: Given: u→=k,5,-1v→=2k,k,3

Q: Find a unit vector that is perpendicular to both u = (1,0, 3) and v = (-1,2,0). Answer:

A: We have to find the unit vector which is perpendicular to given vectors.

Q: Given that u =, and z = What is the x component of the resultant vector w = Зи + 22

A: Given: u=4,-5z=-11,-10

Q: Find the equation of the plane passing through the point (2,−1, 3) and normal to the vector N = (2,…

A: we know that equation of plane which passes through point x1,y1,z1 and normal to vector a,b,c is…

Q: The surface of a hill can be given as h(x, y) = e-(z²+y²), If a ball is placed at the (2, y)…

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Q: Find the horizontal and vertical components of the vector u that has magnitude |u|=4 and direction…

A: Given that, the magnitude is |u|=4 and the direction angle is α=20∘