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What is the angle between vector a and vector b if vector a and vector b denote the adjacent sides of a parallelogram drawn from a point and area of parallelogram is half of ab?
Wiki User
∙ 10y ago
Suppose the angle between the vectors is q
Then area of the parallelogram = a*b*sin q
Therefore a*b*sin q = 0.5*a*b
sin q = 0.5
So that q = pi/6 radians or pi*5/6 radians (30 deg or 150 deg).
Wiki User
∙ 10y ago
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What are four properties of a parallelogram?
#1)The opposite sides of it are always parallel which is to say that they will never intersect. #2)Its area must be twice the area of a triangle created by one of its diagonals. #3)Its area is also equal to the magnitude of the vector cross product of two adjacent sides. #4)Its perimeter of a parallelogram is 2(a + b) where a and b must be the lengths of adjacent sides.
What are the properties of a parallelogram?
The opposite sides of a parallelogram are parallel.The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are equal.The diagonals of a parallelogram bisect one other.The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height.The area of a parallelogram is twice the area of a triangle created by one of its diagonals.The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.Each diagonal bisects the parallelogram into two congruent triangles.It is possible to create a tessellation of a plane with any parallelogram.The parallelogram is a special case of the trapezoid.The rectangle is a special case of the parallelogram.The rhombus is a special case of the parallelogram.
what transformation will always map a parallelogram onto itself?
Linear transformation is a function between vector spaces that will always map a parallelogram onto itself. Some examples are rectangles and regular polygons.
How do you find the area of a parallelogram using 2 vectors?
Given two vectors a and b, the area of a parallelogram formed by these vectors is:a x b = a*b * sin(theta) where theta is the angle between a and b, and where x is the norm/length/magnitude of vector x.
What are the handicaps in solving complicated vector problems by the parallelogram method?
Parallelogram method is not that accurate because a mechanical tool such as protractor is used in constructing the angle of a vector or in other words it is only an illustration unlike in analytical method of adding vectors, mathematical computation is used which is more accurate than making an illustration to present vectors.
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."
In mathematics what does th area of parallelogram is equal to?
IT IS EQUAL TO THE MAGNITUDE OF THE VECTOR PRODUCT OF TWO ADJACENT SIDES
What is the difference between parallelogram law of vector addition n triangle law of vector addition?
There is basically no difference. They are nothing more than 2 different visualizations of how we can graphically add two vectors.strictly if we say there is one and only difference is that---Triangle law of vector addition states that when 2 vectors r acting as the adjacent sides of a triangle taken in order. third side of the triangle will give the magnitude of th resultant 7 direction is in opposite order.Parallelogram law of vector addition states that if 2 vectors r acting as the adjacent sides of a parallelogram, then the diagonal of parallelogram from the point of intersection of two vectors represent their resultant magnitude & direction.
What is the parallelogram law of vectors?
The parallelogram law states that the sum of squares must equal the sum of its four sides. These equations are very complex and hard to understand.
What is the parrallelogram method?
In vector algebra, if you have two vectors, x and y which are not collinear, and x + y is the vector resulting from the two acting together then the magnitude and direction of x+y is given by the diagonal of the parallelogram whose adjacent sides are x and y.If x and y are collinear then the result still hold if you consider the common line as a totally flattened parallelogram.
What are four properties of a parallelogram?
#1)The opposite sides of it are always parallel which is to say that they will never intersect. #2)Its area must be twice the area of a triangle created by one of its diagonals. #3)Its area is also equal to the magnitude of the vector cross product of two adjacent sides. #4)Its perimeter of a parallelogram is 2(a + b) where a and b must be the lengths of adjacent sides.
How can you prove parallelogram inequality?
Try a vector approach.
What are the formulas for the adjacent and the opposite component of a vector?
If a vector, of magnitude v, makes an angle of Φ with the adjacent side then the adjacent component = v*cos(Φ), and opposite component = v*sin(Φ)
How do you graph a vector in component form?
Select two axes in a 2-d plane along which you want the vector components (3 axes in 3-d and so on). The axes must meet at a point, but need not be perpendicular.In 2-d, draw a parallelogram so that its diagonal is the given vector and the adjacent sides are parallel to the axes. These adjacent sides will represent the components of the vector.If the axes are at right angles and the vector Vmakes an angle t with the positive horizontal axis, thenhorizontal component = V*costandvertical component = V*sint
What are the properties of a parallelogram?
The opposite sides of a parallelogram are parallel.The opposite sides of a parallelogram are equal.The opposite angles of a parallelogram are equal.The diagonals of a parallelogram bisect one other.The area, A, of a parallelogram is A = BH, where B is the base of the parallelogram and H is its height.The area of a parallelogram is twice the area of a triangle created by one of its diagonals.The area of a parallelogram is also equal to the magnitude of the vector cross product of two adjacent sides.Each diagonal bisects the parallelogram into two congruent triangles.It is possible to create a tessellation of a plane with any parallelogram.The parallelogram is a special case of the trapezoid.The rectangle is a special case of the parallelogram.The rhombus is a special case of the parallelogram.
what transformation will always map a parallelogram onto itself?
Linear transformation is a function between vector spaces that will always map a parallelogram onto itself. Some examples are rectangles and regular polygons.
What is an algebraic representation of a vector?
There are many algebraic representations that can denote the vector.A number is an algebric representation of a vector, when denoted by a unit vector factor, e.g Av= IAx + JAy + KAz. The unit vectors are I, J and K and these denote the vector. The subscript v as in Av also denotes the vector, other denotations can be Bolding A, as a vector.oI use brackets A= Ar + Av = [a, A] where the upper case is the vector in the brackets and the lower case is the scalar or real.You can use just the comma, A= [5 ,6 4 3] where the real 5 is before the comma and everything past the comma is a vector.There are many algebraic representations that can denote the vector.
