Write an expression for a vector five units long, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the vector i + 2j + 2k.

Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: Find the angle a between the vectors  [ -5 ]    And    [ -2 ] [ 5 ]                 [ 3 ]

A: To find the angle between the vectors

Q: Express the given vector in terms of the unit vectors i, j, and k. (2, -5, 0)

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

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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: Find the unit vector that has the same direction as the vector v = -i + 2j.

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Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: Find the angle a between the vectors -5 and

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Q: Find the angle between the diagonals of a parallelogram constructed on the vectors a=2 i +j and b=-2…

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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: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: Find the component form of the resultant vector. 1) u =(-11, 2) b=(10,-4) Find: -u - b

A: As per guidelines, we'll solve only one question if multiple questions are asked. If you need any…

Q: find the component form of the vector. The sum of AB and CD, where A = (1, -1), B = (2, 0), C = (-1,…

A: Given that A = (1, -1), B = (2, 0), C = (-1, 3), and D = (-2, 2)We have to find AB + CD.

Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

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Q: Determine whether the given vectors are perpendicular. = (0, –7), 3 (8, 0) y = O Yes O No

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Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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Q: Find the unit vector that has the same direction as the vector v = 4i - 2j.

A: the given vector is v=4i-2j

Q: Express the vector as a product of its length and direction. 6j - 8k 100- 10(j - k) 3 10 j O 10(6j -…

A: We have to find out the vector

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

A: a) Given: v1=<-3,6>,…

Q: 3. The dot product of two orthogonal vectors is: A.undefined. B. Zero, C. Infinity.

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Q: Compute the dot product of the two given vectors: 27 1 3. Answer:

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Q: Find the resultant of the vectors A and B. Ả = A = 8a, + 7ay + 2a, B = -Зах — 8ау — ба, Draw the…

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Q: Find the unit vector that has the same direction as the vector v = 3i - 2j.

A: Given vector is v→=3i-2j We have to find unit vector that has same direction as given vector.…

Q: Use paper and pencil to identify the redundant vectors. 2 1 3. 4. 3. 4.

A: We have to identify redundant vectors.

Q: Find the unit vector that has the same direction as the vector v = 8i - 6j.

A: Given vectorv=8i^-6j^

Q: Find the median AD of the triangle ABC where positive vectors of the vertices A, B and C are…

A: Vertices of the Triangle ABC given A=i+j,B=4i+6j,C=i-j; Hence, We can take these vectors as the…

Q: What is the terminal point of the vector a = (4, 1) based at P = (1, 5)? Answer:

A: Use the definition of terminal point, we solve this problem as in next step.

Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: Find the sum of the given vectors; + B Å = 440 N Z 236°, B= 580 N Z 162° Draw and label a diagram…

A: Obtain the graph of vectors as follows: The third arrow is the resultant vector.

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

A: The vectors 4i^-j^, -3i^+2j^

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: C a

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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: Consider two vectors ~a and ~b such that ~a x^b = ~0. What can be said about vectors ~a and b?…

A: We have to give the reasons

Q: The vector i +bj-k is perpendicular to the vector I +2j-3k. what is the value of b?.

A: We know that if two vectors are perpendicular to each other then there dot product is zero. Given,…

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

A: 10,7 and -2,-75

Q: Find two unit vectors that are perpendicular to both j + 2k and i – 2j + 3k.

A: Given that a→=j+2k,  b→=i-2j+3k   We know that the cross product of two vector is perpendicular to…

Q: 27-j+4k sī +2j-2k.

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Q: Find the unit vector that has the same direction as the vector v = 3i - 4j.

A: We have to find unit vector that has the same direction as the vector v=3i-4j. We know that unit…

Q: Determine the angle between the vectors: x 3i + -3j + -7k and y = 12i + 3j +11k

A: x = 3i -3j -7k  y = 12i +3j +11k

Q: Solve for the vector x in terms of the vectors a and b. x + 2a - b = 3(x + a) - 2(2a - b)

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Q: Find the dot product of the vectors v = 5i - 3j and w = 2i - j.

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Q: Consider the vectors a = 4 i+ 8 j-8k, b = 2 i +k and c = 4 j-5k. Are the vectors a and b+c…

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: Find the angle 0 between the vectors a = 8i – j– 4k and b = 2i+j- 9k. %3D

A: A vector is a mathematical concept with both magnitude and direction. It's used to describe things…

Q: Find the angle a between the vectors 3 a || -1 -2 - and 1

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Q: Determine a unit vector perpendicular to the both vectors A - 5i + 6j – 8k and B : - 2i + 5k. |0| =…

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