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Chapter 3: Q39P (page 59)

Vector A鈫�has a magnitude of6.00units, vectorB鈫�has magnitude of7.00units, andA鈫�.B鈫�has a value of14.0What is the angle between the directions of A鈫�and B鈫�?

Short Answer

Expert verified

The angle 胃between A鈫�and B鈫�is 70.5掳.

Step by step solution

01

Vector operations

The dot product of the vectors is equal to the product of the magnitude of the vectors and the cosine of the angle between them. Using this definition, find the value of the angle between the two vectors when the magnitude and dot product are given. The formula for the dot product is,

a鈫�.b鈫�=a.b.c0s胃 (i)

The magnitude of the vector A鈫�is 6.00units. The magnitude of vector B鈫�is7.00units. The dot product of two vector is equal to14.0units

02

Finding the direction between two vectors

Substitute the given values in equation (i)

a鈫�.b鈫�=a.b.cos胃14.0=6.00脳7.00脳cos胃14.0=42脳cos胃cos胃=14.042胃=cos-114.042=70.5掳

Therefore, the angle between the two vectors is 70.5掳.

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Most popular questions from this chapter

A golfer takes three putts to get the ball into the hole. The first putt displaces the ball 3.66mnorth, the second 1.83msoutheast, and the third 0.91m southwest. What are (a) the magnitude and (b) the direction of the displacement needed to get the ball into the hole on the first putt?

For the vectors in Fig. 3-32, with a=4, b=3, and c=5, what are (a) the magnitude and (b) the direction of a鈫�脳b鈫�, (c) the magnitude and (d) the direction ofa鈫�脳c鈫�, and (e) the magnitude and (f) the direction ofb鈫�脳c鈫�? (The z-axis is not shown)

Find (a) 鈥渘orth cross west,鈥� (b) 鈥渄own dot south,鈥� (c) 鈥渆ast cross up,鈥� (d) 鈥渨est dot west,鈥� and (e) 鈥渟outh cross south.鈥� Let each 鈥渧ector鈥� have unit magnitude

A displacement vector r鈫�in the xy plane is long and directed at angle 胃=30掳in Fig.3-26 . Determine (a) the x component and (b) the y component of the vector1.

(a) In unit-vector notation, what is r鈫�=a鈫�+b鈫�+c鈫�if a鈫�=5.0i^+4.0j^-6.0k^, ,and b鈫�=2.0i^+2.0j^-3.0k^ ? (b) Calculate the angle between r鈫�and the positive z axis. (c) What is the component ofa鈫� along the direction of b鈫�? (d) What is the component of b鈫�perpendicular to the direction of b鈫�but in the plane of a鈫�and b鈫� ? (Hint: For (c), see Eq.3-20 and Fig. 3-18)
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