(a)
The angle between the vectors
(a)
Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Write the expression for dot product of
Here,
Rearrange equation (I), to find
Conclusion:
Substitute
Therefore, The angle between the vectors
(b)
The angle between the vectors
(b)
Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Conclusion:
Substitute
Therefore, The angle between the vectors
(c)
The angle between the vectors
(c)
Answer to Problem 12P
The angle between the vectors
Explanation of Solution
Given that
Conclusion:
Substitute
Therefore, The angle between the vectors
Want to see more full solutions like this?
Chapter 6 Solutions
Principles of Physics: A Calculus-Based Text
- If the dot product of two vectors vanishes, what can you say about their directions?arrow_forwardWhich of the following statements is true about the relationship between the dot product of two vectors and the product of the magnitudes of the vectors? (a) AB is larger than AB. (b) AB is smaller than AB. (c) AB could be larger or smaller than AB, depending on the angle between the vectors. (d) AB could be equal to AB.arrow_forwardShow that when A+B=C then A2+B2+2ABcos , where is the angle between vectors A and B .arrow_forward
- (a) For what values of the angle between two vectors is their scalar product positive? (b) For what values of is their scalar product negative?arrow_forwardAnswer the preceding problem using polar coordinates.arrow_forwardUse the definition of scalar product, ?→⋅?→�→⋅�→ = ab cos θ, and the fact that ?→⋅?→�→⋅�→ = axbx + ayby + azbz to calculate the angle between the two vectors given by ?→=6.0?̂ +6.0?̂+6.0?̂�→=6.0�̂+6.0�̂+6.0�̂ and ?→=2.0?̂ +2.0?̂+3.0?̂�→=2.0�̂+2.0�̂+3.0�̂.arrow_forward
- Using the definition of dot product: Ax B= (A,B₂ - A₂By)i + (A₂Bx − AxB₂)j + (AxBy - Ay Bx)k Find the cross product Ax B the following vectors: (a) U A = 11 + 3) + 0k B = 3î + 1ĵ + 0k A = 11 - 3j+2k B = -31 + 1ĵ+ 0k (b) (d) A = 1î + 1ĵ + Ok B = 2î - 3j+0k A = 21-5j-1k B = 3î + 1ĵ+ 3karrow_forwardScalar or dot product of vectors 9i + 6j + - 4k and 1i + 3j + 0k?arrow_forwardUsing the definition of the scalar product, find the angle between the following vectors. (Find the smallest nonnegative angle.) (a) A-21-9) and B=31-5j 24.20 x Your response differs from the correct answer by more than 10%. Double check your calculations." (b) A=-61+ 7) and B=31-4) + 2k 168.35 x Your response is within 10% of the correct value. This may be due to roundoff error, or you could have a mistake in your calculation. Carry out al (c) A=1-21 +2k and B = 3] + 4k 60 X Your response differs from the correct answer by more than 10%. Double check your calculations.arrow_forward
- Find the scalar product between the vectors ? = 5?̂ + 6?̂ + 1? y ? = −3?̂ + 4?̂ − 8?. What is the angle between these two vectors?arrow_forwardCalculate the dot product: A ∙ B, given that vectors A = 3i + 6j a nd B = 4i – 4j (use - sign in answer, if neededarrow_forwardUse the definition of scalar product, a = ab cos 0, and the fact that a . the two vectors given by a = 3.01 +3.0 + 3.0k and b Number i Units = axbx + ab + a₂b₂ to calculate the angle between 4.0î + 9.0ĵ + 7.0k. =arrow_forward
- Principles of Physics: A Calculus-Based TextPhysicsISBN:9781133104261Author:Raymond A. Serway, John W. JewettPublisher:Cengage LearningUniversity Physics Volume 1PhysicsISBN:9781938168277Author:William Moebs, Samuel J. Ling, Jeff SannyPublisher:OpenStax - Rice UniversityPhysics for Scientists and Engineers: Foundations...PhysicsISBN:9781133939146Author:Katz, Debora M.Publisher:Cengage Learning