Find the measures of the angles of the triangle where vertices are A = (-1,0), B = (2,1), C = (1,–20). Also find the projection of vector AB onto AC.

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: The norm of the vector v= - i+10j-8k is ||v||=, (Round your answer correct to 3 decimal places)

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Q: What can be said about the vectors u and v when the projection of u onto v equals u?

A: What can be said about the vectors u and v when the eprojection of u onto v equals u?

Q: Show that the vectors i - j, j - k, k - i are parallel to a plane.

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Q: Find the area of the parallelogram that has the vectors u = ⟨3, −1, 5⟩ and v = ⟨2, −4, 1⟩ as…

A: Now

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: Find a unit vector in the direction of v = ⟨−2, 5⟩ and verify that it has length 1.

A: A unit vector in the direction of v = ⟨−2, 5⟩ is given by v/|v|

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

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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: 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 angle between the vectors u = (1, −1) and v = (0, 1).

A: Given query is to find the angle between the vectors.

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: 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: Consider the points P(2, −1, 0), Q(5, 0, 0), and R(3, 1, √5). Find the coordinates of the vector QS…

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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 the vector v of length 6 that has the same direction as the unit vector (1/2, V3/2).

A: Consider the following values: magnitude=6unit vector=12i^+32j^

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

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Q: Find a vector v that is perpendicular to the plane through the points А %3 (0, 4, —3), В 3 (5, —5,…

A: Coordinator of the plane is given Find out the vector that is perpendicular to the plane

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: For what value of a is the vector v = ⟨4, -3, 7⟩ orthogonal to w = ⟨a, 8, 3⟩?

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Q: Find the values of x such that the angle between the vectors u = (2, 1, -1) and v = (1, x, 0) is…

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Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: Find the vector v with the given length and the same direction as u.||v|| = 3, u = (0, 2, 1, −1)

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Q: Find the unit vector in the direction of v = (3, −1, 2), and verify that this vector has length 1.

A: Vector v = (3, −1, 2) Such that,

Q: Find a vector V of a magnitude equals 14 and perpendicular To the plane in space which includes the…

A: Explanation of the answer is as follows

Q: At what value of k are these vectors collinear?

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Q: Find the angle between the two given vectors. u = (1, –4, 1), v = (0, 2, –2)

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Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

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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: What vector has the same magnitude as the vector u = (4,-3) and points in the opposite direction?

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Q: For what value of c is the vector v = ⟨2, -5, c⟩ orthogonal to w = ⟨3, 2, 9⟩?

A: Two vectors are said to be orthogonal if their dot product is zero.

Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

A: Explanation: Given that,  Vectors v and w length is 3 angle between vectors v and w:…

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: 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 the vector with length V17 and same direction as i= (7,0, –6).

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Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Find v x w, where v and w are vectors of length 3 in the xz-plane, oriented as in the figure below,…

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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),…

A: We find a vector v that is perpendicular to the plane through the points A = (2, 5, 1), B = (5,4,…

Q: Find the vector w which is of length 6 and oppositely directed to u=(2,-2,1) Select one: O None W=…

A: A vector oppositely directed to  u⇀ = <2,-2,1>  is  w = − u = − <2,-2,1>  i.e.  w =…

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

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Q: Find the angle between the vectors u (2, –1) and v = (1, 1).

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Q: Find the area of a parallelogram formed by the vectors PQ and PR, where P = (– 6, – 1, 3), Q = (- 1,…

A: The corresponding position vectors with respect to origin are,…

Q: Given the points X(1, -2, 1) and Y(0, 3, -2), find a vector that is collinear with XY and has a…

A: Given: X(1, -2, 1) and Y(0, 3, -2).

Q: Find the area of the parallelogram that has the vectors as adjacent sides.u = j, v = j + k

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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: Find the area of the parallelogram that has the vectors as adjacent sides.u = i − j + k, v = i + k

A: Given vectorsu = i-j+k , v = i+kArea of parallelogram is equal to u x v

Q: Find the angle θ between the vectors.u = (3, 1), v = (−2, 4)

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Q: Find a vector that is oppositely directed to v = with a length of V3

A: We have to find the vector by given data

Q: Find the vector of length 10 with the same direction as w = (2, V2, V3).

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Q: For the vector PP, , its norm satisfies PP, =2. The inscribed angles between PP, 2 2 and x-axis and…

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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 the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

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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: Use the points P(3, 1) and Q(7, 1) to find position vectors equal to PQ and QP.

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

A: Topic = Vector