Vector Multiplication
Learn about vector multiplication, unit vectors, magnitude calculations, scalar dot products, cross products, and angle determinations between vectors. Explore video explanations and visual representations for a comprehensive understanding of vector mathematics concepts.
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Vector Multiplication Return to Table of Contents https://njctl.org/video/?v=byuPJNfJT1U
Unit Vectors Unit vectors describe directions in space. They do not represent any physical quantity and have a magnitude of 1. indicates the x direction indicates the y direction indicates the z direction Any given Vector can be presented in terms of unit vectors:
Unit Vectors When two vectors A and B are represented by their components in the xyz plane using unit vectors, the resultant vector R = A + B is expressed as: The magnitude of R is: Pythagoras in 3D!
13 What is the magnitude of the sum of the following vectors? A B C D E 9.3 12.3 5.1 10.7 3 C Answer https://njctl.org/video/?v=N0jzk3Wi3Xc
15 What is the closest value for the scalar dot product of vectors A and C ? A B C D E 0 14 42 -14 -42 4 Answer 7 D 6 65o 45o https://njctl.org/video/?v=VspBDduAT44
Vector Cross Product The vector cross product yields a vector quantity and its magnitude is defined as: The cross product can be viewed as the "projection" of the magnitude of A on a line perpendicular to vector B(Asin ), multiplied by the magnitude of B. The magnitude of this product can be positive or zero depending on angle . ranges from 0 to 1800. The vector cross product is a minimum when the two vectors are in line, = 00. It is a maximum when = 900. https://njctl.org/video/?v=N1WKTxZt_xE
Vector Cross Product The vector cross product yields a vector quantity and its magnitude is defined as: Since the cross product results in a vector, it must also have a direction. In previous physics courses, the concept of the "right hand rule" was developed to give this direction. Physicists don't use the right hand rule to solve complex problems - they use the vector cross product.
19 Solve for the angle between vectors and Answer 98o 278o 57o 85o 124o A B C D E A https://njctl.org/video/?v=ak5u5eVQHzs
20 Two vectors are given: The angle between vectors A and B, in degrees, is: Answer o A B C D E 117 o 76 150 o o 29 161 B o https://njctl.org/video/?v=BkKKnh__U9c
21 Two vectors are given: Solve for the magnitude of Answer 33 29 25 21 17 A B C D E A See next slide for worked out solution. https://njctl.org/video/?v=-oJOuHBjJTs
Two vectors are given: Worked Out Solution Solve for the magnitude of
