8. Point P with coordinate (-4, 1) is translated along vector la.6). P' (0, 4). What are the values of a and b?

Q: Find the plane equation through point (3, -1, 7) and perpendicular to normal vector n = (4, 2, 5)

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Q: An athlete standing west of a river flowing from north to south at 0.4 m/s and is 72 m wide swims at…

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Q: Find the shortest distance from point P = (1,2,-3) to the plane which passes through (2,3,-1) and…

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Q: How is the angle between two vectors defined and how is it computed?

A: the angle between two vectors is computed using cosθ

Q: In point P(-6,-8,8), express that vector that extends from P to Q(8, 6, -1) in: a. spherical…

A: Point P(-6,-8,8) and Point Q(8,6,-1) given Let's find vector sperical coordinates.

Q: 2- Suppose that vector v has initial point (-4,5) and terminal point (-1,12). a- Find the component…

A: a)A position vector v→ is defined as a line extending from the initial point (x1,y1) to the final…

Q: (6) calculate the inrtantanco us rate of at point (4,1,2) in the change of 9 direction of the vector…

A: This is a question of multivariable calculus, the calculus of several variables.

Q: Find the unit vector represented by the directed line segment with initial point A (-2,1,1) and…

A: The vectorAB = B-A=(2,-3,4) -  (-2,1,1) = (4,-4,3) So the unit vector is :…

Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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Q: What position vector is equal to the vector from (3, 5, -2) to (0, -6, 3)?

A: We have given two vectors;  (3, 5, -2) , (0, -6, 3)

Q: In point P(-6,-8,8), express that vector that extends from P to Q(8, 6, -1) in: a. cylindrical…

A: Here we have to convert it into cylindrical coordinates.

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

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Q: Determine the equations of the line (vector, parametric, Cartesian and general) that passes through…

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: In point A (-6,-8,8), express that vector that extends from A to B (8, 6, -1) in spherical…

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Q: 2- Are the vectores [4,2,6] and [6, 3, 9] collinear? How do you know?

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Q: what is the parametric and symmetric eqvotions of the line that passes thrs point (4.-3,57 to beth…

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Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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Q: U=(-1,2) as(-2,3) find Hhe vector Comporent Wis Projau

A: Take the help of dot product and use the formula.

Q: The plane with normal vector - 7) containing the point (4,-1,1) has equation Ar + By + Cz = D. If A…

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Q: A plane contains the point  (1, -1,0 ) and its normal vector is \ vec {n} =  (6,24, -8 ). What is…

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Q: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: Resolve the vector of 300N at N25W into its rectangular components. Use right/left and up/down for…

A: Vx = -126.785 Vy = 271.892   explanation is given in below step

Q: If a particle travels along a straight line, then the acceleration and velocity vectors are (choose…

A: To deermine If a particle travels along a straight line then the acceleration  and velocityare

Q: Give a vector of length 13 that is parallel to (-1,2, –2).

A: Topic- vector calculus

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: A hiker begins at the origin and walks in a straight line in the direction of the vector (1,1) for…

A:

Q: a horizontal vector has initial point (-4,1) and has a magnitude of 7. What is the terminal point?…

A: The initial point of the vector is (-4, 1) and the magnitude of the vector is 7. Since it is a…

Q: Find two different vector parametrizations of the line through P = (5, 5, 2) with direction vector v…

A: Given the points are (5,5,2) and the direction vector v=<0,-2,1>Hence, Vector…

Q: Let vector AB = (2,3,1). If the coordinates of A are (2,1,5), what are the coordinates of the point…

A: Vector AB= B-A

Q: Suppose (vector u)=(3,-4,-5) and Vector v=(2,-1,2)u+v=?u-v=?v-u=?3u=?(-1/4)v=?2u-3v=?I appreciate…

A: u=(3,-4,-5)v=(2,-1,2)

Q: The vector with terminal point at P(-5,0,3) and initial point at Q(6, 2, –8) is equal to the…

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Q: The terminal point of the vector v = 3i -j+ 5k with initial point (2, 5, -5) is Do not leave any…

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Q: The unit vector (1,0,0) is initially on the x-axis. If it is rotated in the positive xz direction by…

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Q: What is the component form of the vector whose tail is the point (-1,5), and whose head is the point…

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Q: direction as the vector from the point ?=(0,3) to the point ?=(−2,−2)?

A: Given query is to find indicated vector.

Q: 7. Find a vector that has the same direction as (-2,1, 2) but twice the length.

A: GIVEN DATA : Vector of direction -2, 1, 2       TO FIND : The vector of the same direction but twice…

Q: 5. Verify that its possible for a line with direction vector J=(2,1,-2) to lie flat on a plane with…

A: The vector equation of a plane is given by the expression . Here, and are the vectors that lie on…

Q: Find the unit vector along the line joining point (2, 4, 4) to point ( - 3 , 2, 2). A) -0.8703ax -…

A: We can solve this as follows:

Q: What is the position vector (expressed in RCS), determined by point B(2,30 deg, 3)?

A: Definition: The point A(a,b,c) has a position vector OA where a is the x-component, b is the…

Q: set

A:

Q: ind a vector orthogonal to the plane containing points (3, 1, 1), (4, 0, 2), (6, 3, 1).

A: Given problem:- Find a vector orthogonal to the plane containing points (3, 1, 1), (4, 0, 2), (6, 3,…

Q: The vector (1, 0, 0) makes a 45 degrees with the vector (x, y, z). What is the relationship between…

A:

Q: A direction vector passes through a unit cube from the (1/4, 1, 1/4) to the (1, 0, 3/4) positions.…

A: The direction passes through a unit cube from the 14,1,14 to the 1,0,34 positions. We have to find…

Q: What is the component form of the vector whose tail is the point (-3, 2) and whose head is the point…

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Q: Is the line passing through the point (3/2, 1) and slope −2 a hyperplane ? If yes, identify this…

A: Any line in 2D is a hyperplane.  ax+by=c, is a hyperplane (a,b) is called the normal vector  c is…

Q: A vector with magnitude 4 points in a direction 265 degrees counterclockwise from the positive x…

A: Given  Magnitude of 4 points at an angle of 265° In counter clockwise direction  from positive x-…

Q: to Dara bala y=XZ. Find the unit vectors that are parallel to the tangent line Dara bola y = x² at…

A:

Q: Evaluate the directional derivative Duf (2, 3) if ƒ (x, y) = and u is the unit vector in the same…

A: Given problem:- Evaluate the directional derivative Duf(2, 3) if f(x, y) = x/(x2 - y) and u is the…

Q: Find an equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…

A: Given An equation of the plane that passes through (4,-1,2) and has a normal vector perpendicular to…