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Show that the sum and difference of two prependicular vectors of equal length are also perpendicular of same length?
Wiki User
∙ 12y ago
yes ithape ens only if the two vectors are perpendicular to eachothe we can equate their squares
Wiki User
∙ 12y ago
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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.
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
When adding vectors in one dimension what does the length of arrows represent?
The magnitudes of the vectors. apexs
When adding vectors in one dimension which the following could the length of the arrows represent?
The length of the arrows could represent either the magnitude or the direction of the vectors. If the length represents magnitude, longer arrows would represent larger magnitudes of the vectors. If the length represents direction, the arrows would be all the same length, but pointing in different directions to represent different vectors.
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.
Is the sum and difference of two perpendicular vectors have same lengyhs and also perpendicular to each other?
Yes, the sum of two perpendicular vectors has the same length as the original vectors, and they are also perpendicular to each other. However, the difference of two perpendicular vectors may not have the same length as the original vectors, but they will still be perpendicular to each other.
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.
What is the dot product of two perpendicular vectors vector a and vector b respectively?
The dot product of two perpendicular vectors is 0. a⋅b = |ab|cos θ where: |a| = length of vector a |b| = length of vector b θ = the angle between the vectors. If the vectors are perpendicular, θ = π/2 radians → cos θ = cos(π/2) = 0 → a⋅b = |a| × |b| × 0 = 0 ----------------------------------------------------------------------------- The dot product can also be calculated for vectors of n dimensions as the sum of the products of the corresponding elements: a = (a1, a2, ..., an) b = (b1, b2, ..., bn) a⋅b = Σ ar × br for r = 1, 2 , ..., n With perpendicular vectors this sum is zero,
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.
Difference between orthogonal and perpendicular lines?
Orthogonal and perpendicular are essentially the same thing: When two lines, planes, etc. intersect at a right angle, or 90 degrees, they are orthogonal/perpendicular.Orthogonal is simply a term used more commonly for vectors, when they have a scalar/inner/dot product of 0, as:vector u X vector v = (length of vector u) X (length of vector v) X cos @ ,@ being the angle between the two vectors.When the scalar product is 0, that is because @ is 90 degrees, and cos 90 = 0. Therefore, the vectors u and v are orthogonal.
When adding vectors in one dimension what does the length of arrows represent?
The magnitudes of the vectors. apexs
Are the diagonals of a rhombus perpendicular and bisect each other?
Yes, they are perpendicular and intersect at their midpoints. The difference between diagonals in a rhombus as opposed to a rectangle or square is that the diagonals are not of equal length.
When adding vectors in one dimension which the following could the length of the arrows represent?
The length of the arrows could represent either the magnitude or the direction of the vectors. If the length represents magnitude, longer arrows would represent larger magnitudes of the vectors. If the length represents direction, the arrows would be all the same length, but pointing in different directions to represent different vectors.
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.
Can the magnitude if the difference between two vectors ever be greater than the magnitude of their sum?
No, the magnitude of the difference between two vectors cannot be greater than the magnitude of their sum. This is due to the triangle inequality, which states that the magnitude of the sum of two vectors is always greater than or equal to the magnitude of their difference.
The hypotenuse of a right triangle has a length of 17cm The sum of the length of its perpendicular sides is 23cm What are the lengths of the perpendicular sides?
28.611
Why are vectors considered to be vectors?
Vectors are considered vectors because they have both magnitude (size or length) and direction. This property distinguishes vectors from scalars, which only have magnitude. In physics and mathematics, vectors are essential for representing physical quantities like force, velocity, and displacement that have both size and direction.
