Introduction to rotate vector by angle:
When a vector is rotated by an angle the angle between the original vector and the newly formed vector can be calculated using the formula for calculating the dot product of the original vector and the newly formed vector. In the following article we will see in detail about the topic rotate vector by angle. Understanding Adding Vector Components is always challenging for me but thanks to all math help websites to help me out.
More about Rotate Vector by Angle:
In math the vectors are the geometric quantities with both the magnitude as well as the direction. When a vector is rotated by an angle a new vector is formed and the two vectors will be having the same vertex point. So the angle by which the vector is rotated is calculated by using the dot product of the vectors formula. And the formula for the dot product of the vectors is given by,
`A*B = |A| |B| Cos theta`
The formula can also be written as,
`Cos theta = (A*B)/(|A| |B|)`
So for calculating the angle θ between the two vectors will be
`theta = arccos [(A*B)/(|A| |B|)]`
Example Problem on Rotate Vector by Angle:
1. Calculate the angle between the vectors A = 1i + 3j + 3k and B = 2i - 2j + 4k.
Solution:
The angle between the vectors theta = `arccos [(A*B)/(|A| |B|)]`
`A*B = (2i + 3j + 3k)*(2i - 2j + 4k)`
`= 1*2 + 3*-21 + 4*3`
`= 2-6+12`
`= 8`
`|A| = sqrt(1^2 + 3^2 + 3^2) = sqrt(1+9+9) = sqrt (19)`
`|B| = sqrt(2^2 + (-2)^2 + 4^2) = sqrt(4+4+16) = sqrt (24)`
`theta = arccos [(A*B)/(|A| |B|)]`
`= arccos [(8)/(sqrt22*sqrt24)]`
`= arccos (8/22.98)`
`= arccos (0.348)`
`= "69.6 degrees"`
Is this topic algebraic expressions hard for you? Watch out for my coming posts.
Practice problems on rotate vector by angle:
1. Calculate the angle between the 3D vectors A = i - 3j + k and B = 2i - j + 4k having a common vertex point.
Answer: 58.2 degrees
2. Calculate the angle between the 3D vectors A = i - 2j + 3k and B = i + 6j - 3k having a common vertex point.
Answer: 142 degrees
When a vector is rotated by an angle the angle between the original vector and the newly formed vector can be calculated using the formula for calculating the dot product of the original vector and the newly formed vector. In the following article we will see in detail about the topic rotate vector by angle. Understanding Adding Vector Components is always challenging for me but thanks to all math help websites to help me out.
More about Rotate Vector by Angle:
In math the vectors are the geometric quantities with both the magnitude as well as the direction. When a vector is rotated by an angle a new vector is formed and the two vectors will be having the same vertex point. So the angle by which the vector is rotated is calculated by using the dot product of the vectors formula. And the formula for the dot product of the vectors is given by,
`A*B = |A| |B| Cos theta`
The formula can also be written as,
`Cos theta = (A*B)/(|A| |B|)`
So for calculating the angle θ between the two vectors will be
`theta = arccos [(A*B)/(|A| |B|)]`
Example Problem on Rotate Vector by Angle:
1. Calculate the angle between the vectors A = 1i + 3j + 3k and B = 2i - 2j + 4k.
Solution:
The angle between the vectors theta = `arccos [(A*B)/(|A| |B|)]`
`A*B = (2i + 3j + 3k)*(2i - 2j + 4k)`
`= 1*2 + 3*-21 + 4*3`
`= 2-6+12`
`= 8`
`|A| = sqrt(1^2 + 3^2 + 3^2) = sqrt(1+9+9) = sqrt (19)`
`|B| = sqrt(2^2 + (-2)^2 + 4^2) = sqrt(4+4+16) = sqrt (24)`
`theta = arccos [(A*B)/(|A| |B|)]`
`= arccos [(8)/(sqrt22*sqrt24)]`
`= arccos (8/22.98)`
`= arccos (0.348)`
`= "69.6 degrees"`
Is this topic algebraic expressions hard for you? Watch out for my coming posts.
Practice problems on rotate vector by angle:
1. Calculate the angle between the 3D vectors A = i - 3j + k and B = 2i - j + 4k having a common vertex point.
Answer: 58.2 degrees
2. Calculate the angle between the 3D vectors A = i - 2j + 3k and B = i + 6j - 3k having a common vertex point.
Answer: 142 degrees
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