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Can the directions of the sum of two two vectors be equal to the directions of difference of two vectors?
Yes.
When is a cross product zero?
When the component vectors have equal or opposite directions (sin(Θ) = 0) i.e. the vectors are parallel.
The sum of two vectors is a minimum when the angle between them is what?
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
What is parallelogram law of vectors?
"If two vector quantities are represented by two adjacent sides or a parallelogram then the diagonal of parallelogram will be equal to the resultant of these two vectors."
When are two vectors identical?
Two vectors are identical when all their components are identical. An alternative definition, for vectors used in physics, is that they are identical when both the magnitude and the direction are identical.
What are unit vectors?
a unit vector is a vector which has exact same direction and has its length or magnitude equal to one
What are unit vectors used for in real life?
In real life unit vectors are used for directions, e.g east, north and up(zenith). The unit vector specifies the direction. Gyroscopes maintain a direction and keep things level. Whenever and where ever location is important, unit vectors are a part of real life. Whenever directions are important in your real life, then unit vectors are important. If everything was confined to move along a straight line, then unit vectors would not be important. If you can move in a plane, then unit vectors are important. Moving in space, unit vectors are more important. cars, ships and planes all move in space. Controlling and tracking these all involve unit vectors.
When do we use vector algebra in daily life?
In real life unit vectors are used for directions, e.g east, north and up. The unit vector specifies the direction. Gyroscopes maintain a direction and keep things level. Whenever and where ever location is important, unit vectors are a part of real life. Whenever directions are important in your real life, then unit vectors are important. If everything was confined to move along a straight line, then unit vectors would not be important. If you can move in a plane, then unit vectors are important. Moving in space, unit vectors are more important. cars, ships and planes all move in space. Controlling and tracking these all involve unit vectors.
What is the difference between orthogonal and orthonormal vectors?
All vectors that are perpendicular (their dot product is zero) are orthogonal vectors.Orthonormal vectors are orthogonal unit vectors. Vectors are only orthonormal if they are both perpendicular have have a length of 1.
Is direction is important for equal vectors?
Equal vectors are vectors having same direction of action or orientation as well as same magnitude. If two or more vectors have same magnitude but different direction then they cannot be called equal vectors. This shows that direction is important for equal vectors.
Can you add equal vectors?
Yes, you can add vectors of equal length. Make sure they are equal by both of them having the same magnitude and direction. Otherwise, you can add equal vectors.
What circumstances will three vectors be equal in magnitude?
If they all have the same norm.
Can the resultant of two equal vectors be of same magnitude as the two vectors?
No, the resultant of two equal vectors will have a magnitude that is not equal to the magnitude of the original vectors. When two vectors are added together, the resulting vector will have a magnitude that depends on the angle between the two vectors.
When are two vectors said to be equal?
If two vectors are represented by the same magnitude and direction they are said to be equal.
For any triangle made of vectors will any pair of vectors that form its sides be equal vectors?
No. Only in the equilateral case. And then they will only be equal in magnitude, not direction.
Can the sum of two equal vectors be equal to either of the vectors?
Only if one of them has a magnitude of zero, so, effectively, no.
What is the relationship between the components of a vector and the unit vectors in a given coordinate system?
In a given coordinate system, the components of a vector represent its magnitude and direction along each axis. Unit vectors are vectors with a magnitude of 1 that point along each axis. The relationship between the components of a vector and the unit vectors is that the components of a vector can be expressed as a combination of the unit vectors multiplied by their respective magnitudes.
