xplain categories of equilibrium? efine a dot product of two vectors A and B, here A = Axi + Avi + Azk and B = Bxi + Byi

Q: The 4.3-kN force F is applied at point A. (a) Compute the moment of F about point O, expressing it…

A: GivenForce applied at A, F=4.3 kNxA=1.2 m, yA=1.8 ma=7, b=11

Q: Dot Product, polar coordinates: If A = 8 < 21 degrees and B = 5 < 62 degrees, find А-В

A: We will first convert the polar coordinates into the cartesian coordinates. Using these coordinates…

Q: The vector orthogonal to 8 +7 and 8 +8 is

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Q: Determine the a.) Dot Product and b.) Cross product of the following given vectors. Given: A = 5i –…

A: Given: A=5i-2k+2jB=2i+1k+2j

Q: Q(2) Consider the two vectors A= 31 - B =-i-4j, Calculate the angle between vectors A) 146" B) 47,7…

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Q: Determine the a.) Dot Product and b.) Cross product of the following given vectors. Given: А 3D 5i -…

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Q: Consider two vectors F = – 2i + 3j – k, and S = 4i – 3j + 2k. The dot product F.S =

A: Given that, F =  - 2i + 3j - k S = 4i - 3j + 2k The dot product of F·S is given by…

Q: Let R Sx TŤ and e tails at the same point. Which of the following is NOT true? 90° is the angle…

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Q: If AxB = 3 A.B, then the angle between the vectors A and B is: o 84.3 071.6 63.4° 076.0

A: Given : |A→×B→| = 3A→.B→       .....(1)To find :Angle between the vectors A→ and B→

Q: Two vectors are given by A = 4 î + 7j and B - -6 i + 2j. (a) Find AxB. (b) Find the angle between A…

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Q: In the cross (or vector) product F = q V X B weknow that q = 1 F = -69î + -27j + -48R - 8.0î + 8.0j…

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Q: 1. a) Find the angle between these vectors. A=2i+3j+k_ve B=i+2j-k b) Find Ax B.

A: Since there are multiple questions posted, we will answer the first question for you. If you want…

Q: + The dot produet of any two vectors as 4 and 4 can be written as: A: 4.4, 4,A, cos0 c 14 x 4= 4,4,…

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Q: Calculate the angle between vectors A=î+3ĵ+2k and B=î+27+3R

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Q: A force is specified by the vector F = (115i + 70j - 170k) N. Calculate the angles made by Fwith the…

A: Given,Force,  F = 115 i^ + 70 j^ - 170 k^ N

Q: Find the angle between the two vectors Ả = 2 î + 3ĵ + k B = -4 î + 2ĵ – k and

A: Given  A=2i+3j+k B=-4i+2j-k

Q: - prove that B.

A: Given, two vector A and B Let angle between a and B is θ

Q: (-2/3,2) 2) (7,-7) 1)

A: To find the polar coordinate for these: Using, x=rcosθy=rsinθr=x2+y2Where,x,y are cartesian…

Q: Determine if each of the following sets of vectors is linearlyindependent or linearly…

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Q: ihow how to resolve the force F into components acting along the u and v axes using the…

A: Using cosine rule,

Q: a Anguarm om entum of a partice, reative b the orig in ofa certain coordinate system is defined as…

A: Given: Angular momentum of a particle, relative to the origin of a certain coordinate system is…

Q: Given the two vectors: A=[4.2, 3.5. –2.2] and B=[–3.8, –9.1, 2.4]. Which is the following is the…

A: We have a vector A which is given by A→=4.2i^+3.5j^-2.2k^ and a vector B which is given by…

Q: Using the vectors u = (-1,0, 1) and &= (0, 1,0) solve the following problems

A: Given     u = (-1,0,1)  v = (0,1,0)  Now ....5u = (-5,0,5)  4v = (0,4,0)

Q: What is the vector product of the following vectors? Show your solution A = 3i+5j - 2k and B = −4i +…

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Q: In unit vector notation, å, and åz vectors are given as å, = -3î + 6ĵ + 2k and åz = -2î – 5j + 2k.…

A: Introduction : Angle between two vectors can be found by taking their dot products. Given :…

Q: If the cross product of two vectors vanishes, what can you say about their directions?

A: Let say we have two vector A &amp; B  having magnitude |A| &amp; |B| and between  these vector angle…

Q: A (-3; 2; 0), B (0; D; 6), C (2; -3; 0) and D (0; -3; 0), Since FBA = 152, FBC= 201 and FBD 192,…

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Q: Show that when A⃗ +B⃗ =C⃗ A→+B→=C→, then C2=A2+B2+2ABcosφC2=A2+B2+2ABcosφ, where φφ is the angle…

A: Given:-  A→+B→= C→ Find:-  Show that C2 = A2+B2+2ABcosφ here φ is the angle between vectors A→ and…

Q: If A C =-11.1, A = 3i -43, and C= 6.5, the angle between the two vectors when they are drawn…

A: The dot product of the two vectors is  A→ . B→ = A B cos θ where, θ is the angle between the two…

Q: A force F = (3i jN acts on a particle that undergoes a displacement given with Ar = (3i + 2j) m.…

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Q: Two vectors Á and B have precisely equal mag- nitudes. For the magnitude of A + B to be 100 times…

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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: Which of the following is conserved if the Lagrangian of the system is given as: 1 L=-m(x° + y*…

A: If the Lagrangian of the system is given, then the Lagrange's equation is defined as follows:

Q: Given M = 5 î + 2 ĵ – 5k and N = 3 î - 4 j - 3 k, calculate the vector product M x N. %3D +

A: The given vectors are: M→=5i^+2j^-5k^N→=3i^-4j^-3k^

Q: Find the angle between these given vectors: u3D{7.19] v- (12,-5]

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Q: vector algebra dot product of (i+j+k) and (i-j+k) is?

A: Given : Vector 1 →V1→=i^+j^+k^ Vector 2 →V2→=i^-j^+k^

Q: Prove That AX B = A xB w hen Yotaing The axles (x, Y, Z) bY an Angle $ a bou The axis Z wherens A-…

A: for rotation of axisusing the equations:x'=xcosθ+ysinθy'=-xsinθ+ycosθz'=z

Q: Two vectors in Cartisian coordinates have components A= (2,2,3) and B =(4,-1,7). What is the dot…

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Q: What is vector producer between vector (A) = 2.00 (i) + 3.00 (j) + 1.00 (k) and vector (B) = 1.00…

A: According to question --- Given that -- vector A = 2i +3j + 1k. vector B = 1i -3j - 2k . We have…

Q: Find two unit vectors that are orthogonal to both u=3I + 2j - 4k and v=-6I +3j + k. What is the…

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Q: Given points A(1,-2,3), B(3,-4,-6) and C(-2,3,5) Find: 1. RAB, RBc and RaC 2. Unit vectors of the…

A: We have 3 points A(1,-2,3), B(3,-4,-6), C(-2,3,5) and their corresponding vectors rA→=i^-2j^+3k^ ,…

Q: Find the direction cosines of angles from x, y, and z axis of the force F = 350N and passing through…

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Q: Given vectors ū = [-2,3,1] i = [1,2, –2] and w = [4, –2, –1] find: b) ü w b) the angle between i and…

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Q: Given M = 6 î + 5 j – 6 k and N = 3 î - 3 j – 3 k, calculate the vector product M x N.

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Q: alForm the dot Product of À- 23N37° and B=14N- b) Form the Cross product of A=23km 3プ and kN 0. 193°

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Q: Find the angle between these given vectors: u-{2,-3,5) v- (6,5,-3] %3D

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Q: Given two vectors A = 2ax + 4ay 10az , B = - $ ap + ap - 3az, and point P(0,2, - 5 ) The angle…

A: Given two vectors A-2ax +4ay +10az and B-5 ap+ad-3az, and point p -(0,2,-5) The angle between A and…

Q: Prove the property of the cross product u × v = 0 if and only if u and v are scalar multiples of…

A: The cross product property of vectors is given by:u×v=uvsinθ......(1)where,u and v are the magnitude…