Let 3i−j+ 4k, 7j−2k, i−3j+k be three vectors with tails at the origin. Then theirheads determine three points A, B, C in space which form a triangle. Find vectors representing the sides AB, BC, CA in that order and direction (for example, A to B, not B to A) and show that the sum of these vectors is zero.

Q: The following two vectors ä = i + 5j – 3k m and b = 5i – j+ 2k m form two edges of a triangle when…

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Q: Consider two vectors ā = 4i – 5j + 2k and b = -2i + 2j + 7k. Find (a) ä + b (b)ā – b, and () a thicd…

A: Given vectors are  a→ = 4i^-5j^+2k^b^ = -2i^+2j^+7k^

Q: : Let x and y be non-parallel vectors. Prove that (x + y) and (x - y) are vectors perpendicular to…

A: For two vectors A→ and B→, the angle between them is θ. The dot product of these vectors…

Q: Two vectors, r and s lie in the xy plane. Their magnitudes are 3.46 and 3.57 units, respectively,…

A: Two vectors can be multiplied in two ways, as a scalar product and as a vector product. In a scalar…

Q: Two vectors, T and s lie in the xy plane. Their magnitudes are 4.85 and 4.39 units, respectively,…

A: Given data: The magnitdue of vector r = 4.85. The magnitdue of vector s = 4.39. Direction of r is…

Q: Consider the vectors A = (-5.4, 8.8) and B = (8.7, -9.4), such that A - B + 3.8C = 0   What is the x…

A: Let the coordinates for point C be (x, y).For the given coordinates of A and B, vector…

Q: Consider the vectors A = 6i + 3j and B = 3î - 6j.

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Q: Given vectors: A = 3 i + j – k, B = - i + 2 j + 5 k, C = 2 j – 3 k.  Find: 1) C ٠ (A + B) 2) C x…

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Q: For the vectors u=i+3j+2k and v=2i−2j+2k calculate  projvu and scalvu

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Q: If a particle moves from point P (2,3,5) to point Q (3,4,5). Its displacement vector be * O i+j+ 10…

A: Explanation and formula :- When a particle moves from a point Ax1,y1,z1 to a point B x2, y2, z2 then…

Q: Given that u is a vector of magnitude 2.5, v is a vector of magnitude 3 and the angle between them…

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Q: Given two vectors A and B. Find the angle between them if A = {2, -3, 4} and B = { -1,2, -2}. be…

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Q: Given the two points P(1,2,3) and Q(2,-2,1) find the vectors

A: Tail of both 'vector lies on origin

Q: Two vectors, r and s lie in the xy plane. Their magnitudes are 3.41 and 5.16 units, respectively,…

A: Given data: The magnitude of vector r is 3.41 units. The magnitude of vector s is 5.16 units. The…

Q: Given two vectors A = 6i + 9j – 7k and B = –123 – 5k, the magnitude of the vector sum is:

A: Given data:  Two vectors  A = 6i + 9j - 7k B = -12j - 5k Required: The magnitude of the vector sum

Q: If A = 4i − 3k and B = −2i + 2j − k, find the scalar projection of A on B, the scalar projection of…

A: The given vectors are, A=4i-3kB=-2i+2j-k

Q: Given vectors A=21+3j+k and B= k and find B*A

A: The 2 vectors are given asA = 2i⏞ + 3j⏞ + k⏞B = k⏞ They have asked for the cross product of the 2…

Q: 4 A -2 4 -2 Consider the two vectors, A and B, in the figure. The x and y components of both vectors…

A: Addition of two vectors A→=axi^+ayj^+azk^ and B→=bxi^+byj^+bzk^ is given by-…

Q: Three vectors are represented by A, 4.2∠45◦, B, 5.5∠−32◦ , and C, 2.8∠75◦. Determine in polar form…

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Q: What is the angle e between vectors à and B if A = 3 i +4 ĵ and B = 8 î – 6 j?

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Q: What is the angle between two vectors A and B if A=4i + 12j +6k and B= 24i -8j +6k

A: If θ is the angle between two vectors A→ and B→, then cosθ=A→·B→A→B→

Q: Here are three vectors in meters: d→1=-6.50î+8.40ĵ+9.60k̂ d→2=-2.00î-4.00ĵ+2.00k̂…

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Q: What is the angle between the two vectors A = 2i + 3j and B = i- 2j is * A 0° 120° 90° 60°

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Q: Let θ be the angle that the vector A vec. makes with the +xaxis,measured counterclockwise from that…

A: There are two physical quantities in nature- scalar and vector. Scalar quantities are those which…

Q: Two vectors, r and s lie in the xy plane. Their magnitudes are 4.58 and 8.82 units, respectively,…

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Q: Show that the force vectorD ⃗ = (2.0i ^ − 4.0j ^ +k ^ )N is orthogonal to the force vector G ⃗ =…

A: Given The force vector D ⃗ = (2 î − 4 ĵ +1 k̂) N. The force vector G ⃗ = (3 î + 4 ĵ +10 k̂) N. If…

Q: Given the vectors A, B and C. Find the following: A = 3i + 5j − 2k; B = −4i + 2j + 3k ; C = 5i – 8j…

A: We have three vectors that are represented by A→=3i^+5j^-2k^,  B→=-4i^+2j^+3k^  and  C→=5i^-8j-9k^.…

Q: Determine the angle between the directions of vector A = 3.00i + 1.00j and vector B = -3.00i + 3.…

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Q: What is the angle between theses two vectors A = 14i – 5j+11k and B= 3i + 7j + 10k ?

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Q: Given the vectors i =(- 3, 7, 4] and y = [- 6, 0, 8], determine b) proj š. a) The angle between i…

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Q: A=4i+6j+2k B=-2i-4j+0k find A+B and it's direction

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Q: Two vectors are given (a = 6 i – 20 j, b = - 7 i + 10 j). Find a + b, a – b, a vector c such that a…

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Q: Find the angle between the following pair of vectors;  A=-4.00i + 2.00j and B = 7.00i + 14.00j

A: The angle between the two vectors is cosθ=A→·B→A→B→ Here A→ and B→ vectors.

Q: Given two vectors A=3i - 4k and B = -5j. What is the angle between these vectors?

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Q: Let be two vectors, such that a=(3+2j-2k) cm and b=(2î+2j+k) cm, calculate: 1) The angle between the…

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Q: Find the scalar and vector projections of a and b if a = 3i − 3j + k and b = 2i + 4j

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Q: Given the two vectorsA=-8i,-4j,-6k and B=2i,+3j,-7k, find (a) A+B, (b)A-B, and (c)-4A (d)A•B (e)AxB…

A: Given:

Q: The vectors from the origin to the points A, B, and C are i + j, 3i + k, and 4i – 3j – 4k,…

A: We first find the vectors of the sides AB, BC and CA. Then find if any two vectors are perpendicular…

Q: Vectors A ⃗ and B ⃗ are two orthogonal vectors in the xy-plane and they have identical magnitudes.…

A: Given data: A→=3.0i^+4.0j^ A→=B→

Q: Find the component form and magnitude of the vector v with the given initial and terminal points.…

A: Given:-   Initial point: (1, −2, 0)               Terminal point: (1, −2, −3) Find:- unit vector in…

Q: For the pair of vectors, find U + V, U − V, and 4U + 2V. U = −9i + 9j, V = 9i + 9j

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Q: show that the vectors A= 1/2 q1+ 1/2 q2+1/2 q3+ 1/2 q4 and B= 1/2 q1 - 1/2 q2 + 1/2 q3 - 1/2 q4 .…

A: Dot product is defined as: A⇀.B ⇀ = ABcos(θAB) The dot product of orthogonal vectors is 0, since the…

Q: These are the component forms of vectors u and w: ū = (–4, −3) = w = (-1,5) Add the vectors. u + w =

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Q: Given vectors M = 2i + 6j and N = i + 2j. Calculate the angle that vector C = M – 2N makes with the…

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Q: If a = i + 3j − k, b = 2i + 4j − 2k and c = −i + 2j + 4k, find a number λ such that d = a + b + λc…

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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.