Vectors (from Activity) Flashcards

1
Q

Find the magnitude of vector V = 2i- 5j.

A

√29 or approximately 5.39

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2
Q

Find the direction cosines and direction angles of the vector A = 2i- 3j + 4k.

A

i = 0.37, j = -0.56, k = 0.74, θi = 68.20°, θj = 123.85°, θk = 42.03°

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3
Q

Find the dot product of the vectors A= 3i + 4j- k and B = i + 2j + 3k.

A

8

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4
Q

Find the angle between the vectors A= 3i + 4j- k and B = i + 2j + 3k.

A

65.21°

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5
Q

Find the vector product( cross product ) of the vectors A= 3i + 4j- k and B = i + 2j + 3k.

A

14i - 10j + 2k

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6
Q

Find the sum of the 2 vectors A = 3i- 5k and B = 2i + 4j- k.

A

5i + 4j - 6k

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7
Q

A force vector F = 2i + 3j is applied to a particle and its moves the particle from ( 1, 2 ) to ( 5, 8 ). Find the work done by the force. Force in N and distance in m.

A

26 J

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8
Q

Find the area of a parallelogram with vertices at A( 1, 2, 3 ), B( 1, 3, 6 ), C( 3, 8, 6 ), and D( 3, 7, 3 ).

A

16.28 m²

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9
Q

Find the volume of a parallelepiped determined by the vectors a=  6, 3,- 1 , b = 0, 1, 2 , and c =  4,- 2, 5 

A

82 m³

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10
Q

The vectors A = 2i- yj + 5k is parallel to vector B = 4i + 6j + 10k. Find y.

A

-3

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11
Q

Angle between vectors formula

A

cos⁡θ= (A * B)/|A||B|

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