a) State the laws of cosine and sine

Q: Find the angle between the vectors A = −2i + j − 2k and B = 2i − 2j.

A: Now angle between the two vectors will be , cos-1a→·b→a→b→

Q: Find the angle between each of the vector pairs: A) A = -2.00i + 6.00j and B = 2.00i - 3.00j B) A…

A: Given vector pairs   A) A = -2.00i + 6.00j and B = 2.00i - 3.00j B) A = 3.00i + 5.00j and B = 10.00i…

Q: Two vectors are given by a→=1.5î+5.7ĵ and b→=1.4î+2.2ĵ. Find (a)|a→×b→|, (b)a→⋅b→,…

A: Given,  a→=1.5i⏞+5.7j⏞b→=1.4i⏞+2.2j⏞

Q: Two vectors are given by a = 2.07 + 5.0j and b = 3.0i + 9.0j. Find (a) a x b", (b) a. b", (c) (a* +…

A: Given:a = 2.0 i^ + 5.0 j^ ................eq(1)b = 3.0 i^ + 9.0 j^ ................eq(2)

Q: Two vectors , and F, lie in the xy-plane as shown in the figure below. If F, = 30 units, and F2 = 20…

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Q: Consider the vectors A and B in component form attached below. What is the angle (in degrees)…

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Q: Two vectors (M = 3ax+2a- 5az) and (N = 6ax–2ay-5az), find the perpendicular to these vectors?

A: If given vectors are perpendicular to each other, then their dot product would be zero.…

Q: Find the angle between each of the following pairs of vectors (round up your answer to the nearest…

A: a) The required angle between the vectors is,

Q: Find the direction and magnitude of the vectors. (a) A (5.0 m)x + (-2.0 m)y, (b) B (-2.0 m)x + (5.0…

A: A→ = 5x^ - 2y^ m B→ = -2x^ + 5y^

Q: Consider the vector v→=0.5t8ı^−13t2ȷ^. Using this vector, evaluate the derivative of the magnitude…

A:

Q: Find the angle between each of the following pairs of vectors (1) A = 3.00i + 5.00j (2) A = -4.00i +…

A: 1) A→ = 3i^ + 5j^B→ = 10i^ + 6j^

Q: Find a unit vector parallel to the resultant vectors y, = 12i – 6j + 4k and Y: =- 8i + 3j – 5k.

A: …

Q: Find the resultant of the two vectors of A = 2.45 N, 15.5° N of E and B = 9.51 N, 38.5° E of N,…

A: Given: The magnitude of vector A is 2.45 N. The direction is 15.5 degrees North of East. The…

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 are given by a = 3.3i + 4.1j and b = 6.6i + 5.5j. Find the component of (a) along the…

A:

Q: Given 2 vectors A = 5i-3j and B = -2i+4j find the angle above the x-axis of A+B and lA+Bl note j and…

A: First we find the addition of given vector and after that we find its magnitude

Q: Given the vectors A = -5i - 3j - 8k ; B = 4i - 2j + 3k ; C = 10i -12j - 8k a. Find A x B b.…

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Q: Draw and find the sum of the following four vectors in (a) unit-vector notation, and as (b) a…

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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: Given two vectors with equal magnitudes of 59 and their sum vector 93j. Find the angle between them.

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Q: 3i + 7j – 4k and (a) cos[A•B/AB] and (b) sin¯|A x B|/AB]. (c) Which 4. Two vectors are given by A =…

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Q: Find the angle (direction) of the resultant of these given vectors: a: 3i +6j b: 7i-3j

A: Given that,a=3i + 6jb= 7i - 3jcosθ=a.bab

Q: You are given two vectors A = -3.00i +7.00j and B= 8.00i + 2.00j. Let counterclockwise angles be…

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Q: What is the resultant vector of two vectors where one has a magnitude of 5 cm pointing 60° N of E…

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Q: A = 3.00î + 5.00ĵ and B = 10.00î + 6.00ĵ %3D

A: Answer :  The angle between these two vectors is ∅= 28.072°

Q: Find the angles that vector Ď = (2.5î – 4ĵ + k) m makes with the x-, y-, and z- axes. 0x Oy = = 0₂:…

A: GIVEN: D= 2.5i^-4j^+k^

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: The three vectors in the figure have magnitudes a= 3.20 m, b 2.70 m, and c 10.3 m and angle 0=…

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Q: For the following three vectors, what is 3C · (2 A✕B )?  A= 2.00i + 3.00j − 7.00k  B= −3.00i +…

A: Given, A→=2i^+3j^-7k^B→=-3i^+7j^+2k^C→=3i^-8j^ So we have, 3C→=33i^-8j^=9i^-24j^ and…

Q: For the following three vectors, what is  3⋅C→⋅(2A→×B→)…

A: (2A X B) can be calculated as follows,

Q: Given these two vectors: à = (5.0 m)ï' – (4. 0 m)j° and b = (7.0 m)ï + (9.0 m)ƒ What are (a) the…

A: Since you have posted a question with multiple sub-parts, we will solve first three sub-parts for…

Q: Obtain expressions in component form for the position vectors having the following polar…

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Q: Two vectors are given by á = 5.4i + 5.6j and b = 4.8i + 2.3). Find (a) a x b, (b)a · b,c)(d + b) .…

A: Given vectors: a→=5.4i^+5.6j^b→=4.8i^+2.3j^

Q: Obtain expressions in component form for the position vectors having the following polar coordinates…

A: (a) 13 m at 140° The vector R is given by  R→ = 13cos 140° i^+ sin 140° j^R→ =- 9.96 i^ + 8.36 j^ m…

Q: Add the following 3 vectors together and find the magnitude of the resultant: 5.0 m E, 3.0 m N, 2.0…

A: In the given question, given that three vectors and We have to determine the magnitude of resultant…

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: Find the angle between two vectors A and B given by : A=6i +4f +2k and vector B=3f -5f-3k

A: Here given two vectors A and  B. Given A= 6i+4j+2k and B= 3i-5j-3k We have to find the angle…

Q: Find the angles that vector D⃗ =(2.0iˆ−4.0jˆ+kˆ)mD→=(2.0i^−4.0j^+k^)m makes with the x-, y-, and z-…

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Q: Given the vectors M = -10a, + 4a, – 8a, and N = 8a, + 7a, – 2a,, find: (a) a unit vector in the…

A: Given, M = -10ax +4ay -8azN =8ax + 7ay - 2az

Q: Two vectors are given by a 2.31 + 2.7) and B = 9.07 + 9.8ĵ. Find (a) 7 x B (b) a . b.c)(7 + b ). B.…

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Q: Vector A has a magnitude of 5.00 units, and vector B has a magnitude of 9.00 units. The two vectors…

A: A = 5.00 units B = 9.00 units angle between them(θ) = 50.0o

Q: If Force (-2,3) and Displacement (-5,-3), find the angle in degrees between the two vectors. O 18.61…

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Q: Two vectors A and B have precisely equal magnitudes. For the magnitude of A + B to be larger than…

A: The given condition is,

Q: If the two displacement vectors with magnitudes of 6.0 m and 8m which could not be a possible choice…

A: The resultant of the displacement will lie between the maximum and minimum value of the resultant of…

Q: given two vectors A= -3.00i + 7.00 j and B= 8.00i + 2.00 j. Let counterclockwise angles be positive.…

A: For any vector in a cartesian plane given as A→=Axi^+Ayj^, such that both the components of vector…

Q: Three vectors are given by a = 5.00î + (-4.00)ĵ + (5.00)k, b = 2.00î + (-1.00)ŷ + (3.00)k, and ? =…

A:

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

A:

Scalars and Vectors

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