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What is the term givin to vectors the go in different directions?
Vectors that go in different directions are called orthogonal vectors. This means that the vectors are perpendicular to each other, with a 90 degree angle between them.
What does it mean when the dot product between two vectors is zero?
When the dot product between two vectors is zero, it means that the vectors are perpendicular or orthogonal to each other.
If two vectors are perpendicular to each other then the resultant what?
The direction after adding two equal and opposite vectors is the "Direction" of the two vectors. V=aDirection and Opposite V = OV = - aDirection. Adding the two gives, V + OV= (a-a)Direction = 0 Direction.
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
What are basis vectors in a transform?
Basis vectors in a transform represent the directions in which the coordinate system is defined. They are typically orthogonal (perpendicular) to each other and have unit length. These basis vectors serve as building blocks to represent any vector in the space.
What is the condition when two vectors are addition and subtraction are same magnitude?
The condition is the two vectors are perpendicular to each other.
What is the term givin to vectors the go in different directions?
Vectors that go in different directions are called orthogonal vectors. This means that the vectors are perpendicular to each other, with a 90 degree angle between them.
What does it mean when the dot product between two vectors is zero?
When the dot product between two vectors is zero, it means that the vectors are perpendicular or orthogonal to each other.
If two vectors are perpendicular to each other then the resultant what?
The direction after adding two equal and opposite vectors is the "Direction" of the two vectors. V=aDirection and Opposite V = OV = - aDirection. Adding the two gives, V + OV= (a-a)Direction = 0 Direction.
What is the difference between scalar and vector products of two vectors?
The scalar product (dot product) of two vectors results in a scalar quantity, representing the magnitude of the projection of one vector onto the other. The vector product (cross product) of two vectors results in a vector quantity that is perpendicular to the plane formed by the two input vectors, with a magnitude equal to the area of the parallelogram they span.
When you resolve a vector and what do you get?
You get other vectors, usually perpendicular to each other, that - when added together - result in the original vector. These component vectors are usually along the axes of some selected coordinate system.
What are basis vectors in a transform?
Basis vectors in a transform represent the directions in which the coordinate system is defined. They are typically orthogonal (perpendicular) to each other and have unit length. These basis vectors serve as building blocks to represent any vector in the space.
How do you determine that two vectors are orthogonal?
'Orthogonal' just means 'perpendicular'. You can establish that if neither vector has a component in the direction of the other one, or the sum of the squares of their magnitudes is equal to the square of the magnitude of their sum. If you have the algebraic equations for the vectors in space or on a graph, then they're perpendicular if their slopes are negative reciprocals.
What is a perpendicular vector?
A perpendicular vector is a vector that forms a right angle (90 degrees) with another vector in a given space. This means that the dot product of two perpendicular vectors is zero, indicating that they are orthogonal to each other.
How do you add vectors that are perpendicular?
Vectors can be added graphically: draw one vector on paper, move the other so that its tail coincides with the head of the first. Vectors can also be added by components. Just add the corresponding components together. For example, if one vector is (10, 0) and the other is (0, 5) (those two would be perpendicular), the combined vector is (10+ 0, 0 + 5), that is, (10, 5). Such a vector can also be converted to polar coordinates, that is, a length and an angle; use the "rectangular to polar" conversion on your scientific calculator to do that.
What is the difference between a perpendicular lines and intersecting lines?
Intersecting cross each other whereas perpendicular lines cross at right angles.
What is the difference between normal and perpendicular?
in 2 and 3 dimensions they turn out to be pretty much the same, but what would perpendicular mean in 4 or 6 dimensions? For example a line perpendicular to another intersects it and creates a 90 degree angle, it is also normal and a line can be normal to a plane also. Normal is a more general term that can be used in higher dimensions and other setting where perpendicular might make no sense. For example, if you know what a dot product is that two vectors are normal if their dot product is zero, These may be n dimensional vectors and perpendicular would make no sense. In many more abstract settings normal works but perpendicular would have no meaning at all. There are more technical explanations but I hope to make this answer more intuitive! There is a very slight difference between NORMAL and PERPENDICULAR. Well NORMAL is that perpendicular which is drawn at the contact point between two meeting lines. Its simple as this. For example in case of tangents (which is drawn to find the direction of a point in a curve) the perpendicular draw at the meeting point of the tangent and the curve is called normal. Its like, every normal is a perpendicular but all perpendiculars are not normal. I hope this clears all your doubt.
