Verify that 2j+k is perpendicular to the plane I7, Find a vector perpendicular to the plane II, Find the acute angle between the planes II, and II,

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 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: Use the dot product to determine whether the vectors are parallel, orthogonal, or neither. v= 2j. w=…

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Q: Given the vector u counterclockwise 11-11 = (2, 5), find the magnitude and angle in which the vector…

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Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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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: or what value of t , if any, is the vector (2t, 1) parallel to the vector (4, -1) t =-2 DA. t = 2…

A: Given that vector 2t,1 paralle to the vector 4,-1find t

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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Q: Given the vector u (5, – 2), find the magnitude and - angle in which the vector points (measured…

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Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

A: point = (3,5,-7)n=0 i +1 j + 0 kCartesian equation of plane is Ax+By+Cz+D=0(A,B,C)=( 0,1,0)(x,y,z) =…

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

A: u = (6,-6)   Magnitude of u = ||u|| = √(36+36) = 6√2

Q: 3) Find the angle between A = 2i + 2j – k and B = 6i – 3j + 2k. 4) Determine the unit vector…

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Q: Rewrite the following vectors in term of unit vectors а. ОP %3D (9, -2) b. 0Q = (7,0,8)

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Q: sketch the coordinate axes and then include thevectors u, v, and u * v as vectors starting at the…

A: Given Data The first vector is u=i-k. The second vector is v=j+k.   The expression for the cross…

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

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Q: a) Find a vector that is perpendicular to both w = ỉ – 3+ 3k and i =7+23.

A: As per our guidelines, we can answer only one question. So, here I am answering for a) please repost…

Q: A) Find the angle between the vectors u = 21 +j+9k, v = 61-12j and %3D sketch the vectors and the…

A: Given,u=2i+j+9kv=6i-12jWe know that cosθ=|u.v|u||v||u.v=(2i+j+9k)(6i-12j)u.v=12-12u.v=0Therefore…

Q: Given the vector u 2i + 1j, find the - magnitude and angle in which the vector points (measured…

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Q: Determine a unit vector perpendicular to the plane a =21-6j –3k and b=4i+3j – *

A: Since you have asked multiple questions in a single request, we would be answering only the first…

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: Find the following for the vectors u = - 6i + 7j + V2k and v = 6i – 7j - v2k. a. v•u, v, and u b.…

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Q: A) Find the angle between the vectors u 21+j+ 9k,v 61-12j and %3D sketch the vectors and the angle…

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Q: Determine the angle between the given vectors. a = 3i – 2j, b = 2i + 2j (b) и %3D (1,—4, 2), v %3D…

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Q: A. By using the dot product, find the angle between the vectors u = 4i – 4j + 2k , v = 6i + 8k Eind…

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Q: Show all work to calculate the value of x that makes the two vectors orthogonal to each other. v =…

A: Orthogonal vectors: Two vectors a→ &  b→ are said to be orthogonal if they are perpendicular to…

Q: Determine whether the given vectors are perpendicular. u = 2i, v = -i + 8j %3D %3D Yes No

A: The given vectors are u=2i and v=-i+8j

Q: Find the magnitude of the vector a and the smallest positive angle 0 from the positive x-axis to the…

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Q: In parallelogram ABCD, E is the midpoint of the diagonals. Тext Let AD = ū and AB = v. A D Express…

A: AD⇀=BC⇀=u⇀ AB⇀=DC⇀=v⇀

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

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Q: Given the unit vectors A, B, C,D that are in the same plane. The value of u-(AxB). (C.D)x(AxB).(C.D)…

A: Please see the explanation below

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: Given: 6j, -4i

Q: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

A: Compute the dot product of the vectors v and w, and find the angle between the vectors. v=−10i+j and…

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: Given the vector i = (1, - 3), find the magnitude and angle in which the vector points (measured…

A: The given vector u→=1, -3

Q: If a = 2i+j-k, b=-i+2k, and c=i+2j-2k, (i) Find a unit vector perpendicular to the plane of a and b.…

A: Let two vectors be defined as x=x1i+x2j+x3k and y=y1i+y2j+y3k . The dot product of the vectors, x ,…

Q: Find a unit vector (a) in the direction of v and (b) in the direction opposite of v = 5i + 3j − k

A: Solution:- The given vector is  v→=5i+3j-k we have to find a unit vector in the direction of  a)…

Q: Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the…

A: Consider the given question,

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v+ w.

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Q: Given the vector u = - 6i – 3j, find the magnitude and angle in which the vector points (measured…

A: Here we will find the magnitude and direction of given vector,

Q: (1b) Find vectors v and w such that v is parallel to y, w is perpendicular to y, and x = v + w.

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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: 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: The angle that the x-axis make with the plane containing the following two vectors is A = 4â – 3 B =…

A: To find the angle

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

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Q: Calculate the angle 0 between vectors a and b when a = i – 2j + 2k , b = 2i + 3j + k %3D

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Q: [2] |W1 = |2 W2 = |2 [3] The angle of the vector u perpendicular to the plane formed by the vectors…

A: Note that the cross product, or, vector product of two vectors is perpendicular to both the vectors.…

Q: Find the distance of point A(2/3,2) from the line that passes through the origin and parallel to the…

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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…

A: Given that, u=a1i+b1jv=a2i+b2jw=a3i+b3j

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.