If the projections of vector a on x,y and z −axes are 2,1,2 units respectively, find the angle at which vector a is inclined to the z −axis.

Q: (2) Given u = [2 1 2]T, find a vector v so that the angle between u and v is 60° and the orthogonal…

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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: B) Given the vectors u = 7i+ 2j -k, v = 2i-3j-6k. Find the projection of %3D u onto v.

A: Using projection vector formula.

Q: Given Ā =,B = and C =. Find: a) the scalar projection of B onto C – À b) a unit vector ū in the…

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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: Given the vector u = (1, 2), find the magnitude and angle in which the vector points (measured…

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Q: The vector with length 4 and direction k is Di+Di+ j+ k.

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Q: When the angle between vectors u and v is between 0° and 90°: || You can't tell O t • 0

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Q: find the acute angle between the given linesby using vectors parallel to the lines. y = x, y = 2x +…

A: Here the acute angle between two lines is to be calculated.

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: · 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: 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: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

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Q: Prove the stated property of distance between vectors. d(u, w) <= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: / If A(1,23=1), B(3)6-7), C(233,-3),D(34-3), Cal culate the angle between the vector Projection of…

A: If vector a→ is projected on vector b→ the the formula of vector projection will be…

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: Prove that two vectors v = (a, b) and w = (c, d)are perpendicularif and only if ac + bd = 0

A: We prove the above statement using the concept of dot product or scalar product of two vectors. The…

Q: If A(1,2.-1) B(3.6-7), c(2,3.-3) D(3.4,-3) Calculate the angle between the vector Projection of ÄB…

A: According to question given that A(1,2,-1)B(3,6,-7)C(2,3,-3)D(3,4,-3)Angle between a pair of lines…

Q: The vectors T and N, when defined, (a) are parallel. (b) are orthogonal. (c) have a zero cross…

A: T is the tangent vector and N is the normal vector.  So they are always orthogonal to each other.

Q: The vector u has length 10 and points at an angle of 15∘ The vector v has length 18 and points at an…

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Q: Find the angle between the vectors v and w v = (2, 1, 3)T , w = (6, 3, 9)T

A: We need to find the angle between the two vectors.

Q: Given v = (8, –3) and w = (12, -4), find vector projection of v onto w.

A: Solution; Consider the given vectors :  v = 8, -3 and w = 12, -4 Now, vector projection of v onto w…

Q: For what value of t if any, is the vector 5t, 1] parallel to the vector (4, -1) ?

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Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

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Q: W,X ,Y,and  Z have the position vectors 3i+3j-4k, 4i+j+k, 2i+3k and 3i+j-4k respectively.…

A: The given position vectors areW = 3 i^ + 3 j^ - 4 k^X = 4 i^ + j^ + k^Y = 2 i^ + 3 k^ Z = 3 i^ +  j^…

Q: Consider the vector v = (2, y) in R?. If you rotate the vector by 90-degrees counter-clockwise, then…

A: Given,   v=2,y   in ℝ2.

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: If v = 2i + 4j and w = -2i + 6j, find the vector projection of v onto w.

A: Given vectors are: v = 2i + 4j w = -2i + 6j The formula for the vector projection of v onto w is…

Q: The vectors v = (3, 4) is projected onto the x-axis The length of the projection is %3D A/

A: We have to find

Q: iven belo

A: The value of derivative of vector R→t, R'→t=2e2t-4,6t2,1t-1  Integrating the derivative vector with…

Q: If u, and u2 are orthogonal unit vectors, and v = au, + bu2, find v•uq. = 'n.a v•u,

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

A: According to the problem, we have

Q: Given the vector u (2, 2), find the magnitude and - angle in which the vector points (measured…

A: Given that: u→=2,-2. Therefore, magnitude of the vector is= u→=22+-22=22.

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: Verify that the vector i = ( ) is a unit vector (that is, has length 1). Then determine the…

A: The projection of a vector w in the direction of v is given by v·wv2v

Q: Given vector u (1, 1) and v (6, 2) , determine the value of V + 2u in component form.

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Q: Prove the stated property of distance between vectors.d(u, w) < d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: Given the vector u (- 6, 2), find the magnitude and angle in which the vector points (measured…

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Q: Given the vector u = ( – 5, – 6), find the magnitude and angle in which the vector points (measured…

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

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: Is the vector projection of B onto A, perpendicular to B? Is the angle between projAB and the vector…

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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: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

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: given vectors u=4i-j and v= 3i+3j compute the projection of v onto u?

A: Given, vector u and v

Q: If v · w is negative, what does this say about the angle between v and w? Draw a 3-dimensional…

A: we have been given that v.w is negative which means v · w < 0 which means the angle between v and…

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…