Show work and/or justification for all answers . Let u = -2 3 V = 3 4 5 a) Find a unit vector in the direction of v b) Find the distance between v and w c) Is u orthogonal to w?

Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

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Q: find the given vector  Unit vector ew where w = (24, 7)

A: Given: w=24,7

Q: Find a unit vector (a) in the direction of v and (b) in the direction opposite of v. v = 4i − 5j +…

A: Now magnitude of v is,

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

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Q: Find the value of a so that vectors U = ai + 3j and V = 9i + 9j are perpendicular. a =

A: Given: U=ai+3jV=9i+9jθ=90ο

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

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: Determine the two unit vectors that are orthogonal to i = (1,2). Which two unit vectors are parallel…

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Q: Determine the dot product of vectors a, b when |a| = 5, |b| = 1 and the angle between a and b is…

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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: Determine the angles made by the vector V = (-59)i + (11) j with the positive y-axis. 169.44° O…

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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: Find the magnitude of the vector and the angle 6,0° <0<360°, that the vector makes with the positive…

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Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Find the value of b so that vectors U = 5i +12j and V = 4i + bj are perpendicular.

A: Given :          U=5i+12jV=4i+bj

Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: A. Give the Cross products of the unit vectors (i, j, k).

A: Understanding of cross product of three vectors are required to under this.

Q: find the length and direction (when defined) ofu * v and v * u. u = 2i + 3j, v = -i + j

A: Given: u=2i+3j, v=-i+j we know that cross product of given two vectors p→=ai+bj+ck, q→=xi+yj+zk is…

Q: For what value of t , if any, is the vector (4t, -1) parallel to the vector (4, -1) ? OAt=1 OB. t= 2…

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

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Q: If you three vectors a = i + j + k, b = 2i – j + 3k and c = i – 2j + k , find a unit vector parallel…

A: Given,          The three vectors are a→=i+j+k , b→=2i-j+3k and c→=i-2j+k.

Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

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Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

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Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

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Q: Assume vector V is in standard position, has the given magnitude, and that u is the angle Vmakes…

A: Given: Magnitude |V|=8.5 Angle θ=97°

Q: ind the value of a so that vectors U = ai + 9j and V = 3i + 3j are

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Q: Let v = ai + bj. Show that v/lvl is a unit vector in the direction of v.

A: Consider the following vector: v→=ai^+bj^ Magnitude of vector v→: v→=a2+b2…

Q: Find the value of a so that vectors U = ai + 6j and V 5= 9i + 12j are perpen dicular.

A: Our Aim is to find the value of a so that the vectors U=ai^+6j^ and V=9i^+12j^ are perpendicular.

Q: A vector F = 30 i + 40 j is used to represent a force. Identify a unit vector u that has the same…

A: Note:- To find a unit vector with the same direction as a given vector, simply we divide the given…

Q: Verify the parallelogram law for vectors u and v in R": |u + v|l? + ||u – v||° = 2||u||? + 2||v||?

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Q: If r is equal to 300 mm, Find: 1.) Rectangular form of r in ft 2.) Unit vector of r

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Q: Suppose that u and v are vectors in R' both of length 2V2 v is also? v2. Thenllu + v|| and that the…

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Q: Based on the table below that showcases the value of u and v can you find a vector [h k] that is not…

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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 between the vectors v and w v = (−2, 3, 1)T , w = (1, 2, 4)T

A: Consider the given vectors: Here the objective is to find the angle between vector v and w.

Q: We have three vectors u, v and w in R4: (7a)[6 marks] Are these vectors u, v and w linearly…

A: Solution.

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

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

Q: Assume vector V is in standard position, has the given magnitude, and that u is the angle Vmakes…

A: The vector representation of of vector v with magnitude |v| and the angle θ, made by v with positive…

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: For what value of t, if any, is the vector t, -1 parallel to the vector (4, - 1) ? OAt=- 16 OB. t =…

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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: Find a unit vector that is orthogonal to both u and v.       u = −3i + 2j − 5k,    v = i − j + 4k

A: u=-3i+2j-5k,  v=i-j+4k Now the vector orthogonal to both u and v is, w=u×v=…

Q: Find the unit vector in the direction of v and verify that it has length 1. v = ⟨3 /2, 5/ 2⟩

A: Given vector is v=32,52. To find the unit vector in the direction of v and to verify that it has…

Q: Assuming vector B is 12 units long, vector 4B is:

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Q: Find the angle between the vectors u and v to a nearest degree: u = j + k, v = i + 2j – 3k

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Q: For vectors v and w E R, show that: (a) |u x v||? = ||u||2 ||v||2 – (u - v)2 (b) ||u x v|| =…

A: derive a formula for the magnitude of v×u, for nonzero vectors v,u:…

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…

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…