Chapter 3: Q39P (page 59)

Vector $\vec{A}$ has a magnitude of $6.00$ units, vector $\vec{B}$ has magnitude of $7.00$ units, and $\vec{A} . \vec{B}$ has a value of $14.0$ What is the angle between the directions of $\vec{A}$ and $\vec{B}$ ?

Short Answer

Expert verified

The angle $(θ)$ between $\vec{A}$ and $\vec{B}$ is $70.5 °$ .

Step by step solution

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,

$\vec{a} . \vec{b} = a . b . c 0 s θ$ (i)

The magnitude of the vector $\vec{A}$ is $6.00 units$ . The magnitude of vector $\vec{B}$ is $7.00 units$ . The dot product of two vector is equal to $14.0 units$

Finding the direction between two vectors

Substitute the given values in equation (i)

$\vec{a} . \vec{b} = a . b . \cos θ 14.0 = 6.00 \times 7.00 \times \cos θ 14.0 = 42 \times \cos θ \cos θ = \frac{14.0}{42} θ = \cos^{- 1} (\frac{14.0}{42}) = 70.5 °$

Therefore, the angle between the two vectors is $70.5 °$ .

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Vector $\vec{A}$ has a magnitude of $6.00$ units, vector $\vec{B}$ has magnitude of $7.00$ units, and $\vec{A} . \vec{B}$ has a value of $14.0$ What is the angle between the directions of $\vec{A}$ and $\vec{B}$ ?

Short Answer

Step by step solution

Vector operations

Finding the direction between two vectors

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

Short Answer

Step by step solution

Vector operations

Finding the direction between two vectors

One App. One Place for Learning.

Most popular questions from this chapter

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Quantum Physics

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Study anywhere. Anytime. Across all devices.

Vector $\vec{A}$ has a magnitude of $6.00$ units, vector $\vec{B}$ has magnitude of $7.00$ units, and $\vec{A} . \vec{B}$ has a value of $14.0$ What is the angle between the directions of $\vec{A}$ and $\vec{B}$ ?