Q1.23 Consider the vector products AX (BXC) and (AXB) Xč. Give an example that illustrates the general rule that these two vector products do not have the same magnitude or direction. Can you choose vectors A, B, and such that these two vector products are equal? If so, give an example.

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annyong558Lv10

25 Nov 2023

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Nelly StrackeLv2

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Related questions

Original Question:

What are the angles between the negative direction of the y axisand (a) the direction of A, (b) the direction of the product A Ã B,and (c) the direction of A Ã (B + 3.00k)?

Cramster Answer:

Since the 130Â° is measured counterclockwise from the +x axis, onemay write the vectors as
A = 8.00(cos130Â°i + sin130Â°j) = -5.14i + 6.13j
B = Bxi + Byj = -7.72i -9.20j.

a) The angle between -j and the direction of A is
? = arccos(A Â· -j/A) = arccos(-6.13/v(-5.142 + 6.132) )
= arccos(-6.13/8.00) = 140Â°.

b) Since the y axis is in the xy plane, and AxB is perpendicular tothat plane, the angle is 90Â°

c) The vector can be simplified to
Ax(B + 3.00k) = (-5.14i +6.13j)x(-7.72i -9.20j +3.00k)
= 18.39i + 15.42j + 94.61k
The magnitude of the vector is v( i2 + j2 + k2) = 97.6.
The angle between -j and the vector is
? = arccos(-15.42/97.6) = 99.1Â°

MY QUESTION:

What is the equation used in part C) of this problem?

It seems that it should be sine to me though I know the answer forthis problem is correct because the book has the answer. I wouldthink to find the direction of A Ã (B + 3.00k) you would:

1) Use the cross product including the k.

2) Then find the magnitude.

3) Finally use the equation AxB=absin(theta)

What is the correct equation to use?

Please also include an explanation. Thanks!

Object A collides on a horizontal frictionless surface with an initially stationary target, object X. The initial and final velocities of object A are shown. The final velocity of object X is not given.

a). At an instant during the collision, is the net force on object A zero or non-zero?

b) [During the collision, is the momentum of object A conserved? Explain. Is the momentum of the system consisting of objects A and X conserved? Explain. On the same horizontal surface, object C collides with an initially stationary target, object Z. The initial speeds of objects C and A are the same, and m_x = m_z > m_A = m_c. After the collisions, object C moves in the direction shown and has the same final speed as object A. In the space below, copy the vectors v_C1 and v_cr with their tails together. Use these vectors to draw the change in velocity vector for glider C, Delta v_c. Is the magnitude of the change in velocity vector of object A greater than, less than, or equal to the magnitude of the change in velocity vector of object C? Explain? Is the magnitude of the change in the momentum vector of object A greater than, less than, or equal to the magnitude of the change in the momentum vector of object C? Explain? Is the final speed of object X greater than, less than, or equal to the final speed of object Z? Explain. Consider the following incorrect statement: Gliders A and C have some change in momentum. They have the same mass, and because they have the same initial speed and same final speed. Delta-v is the same for each of.them." Discuss the error(s) in the reasoning.

sangriaporcupine175

Let the four compass directions north, east, south, and west be represented by unit vectors , , , and , respectively. Vertically up and down are represented as \hat{u} and \hat{d}. Let us also identify unit vectors that are halfway between these directions such as for the northeast. Rank the magnitudes of the following cross products from largest to smallest. If any are equal in magnitude or are equal to zero, show that in your ranking.