How do you find the area of two vectors?
How do you find the area of two vectors?
The cross product
- a×b is a vector that is perpendicular to both a and b.
- The magnitude (or length) of the vector a×b, written as ∥a×b∥, is the area of the parallelogram spanned by a and b (i.e. the parallelogram whose adjacent sides are the vectors a and b, as shown in below figure).
What is law of triangle for vector addition?
Triangle law of vector addition states that when two vectors are represented as two sides of the triangle with the order of magnitude and direction, then the third side of the triangle represents the magnitude and direction of the resultant vector.
How I calculate the area of a triangle?
The area of a triangle is defined as the total region that is enclosed by the three sides of any particular triangle. Basically, it is equal to half of the base times height, i.e. A = 1/2 × b × h.
What does the cross product of two vectors represent?
Cross product formula between any two vectors gives the area between those vectors. The cross product formula gives the magnitude of the resultant vector which is the area of the parallelogram that is spanned by the two vectors.
How do you find a area of a triangle?
Triangle area formula A triangle is one of the most basic shapes in geometry. The best known and the simplest formula, which almost everybody remembers from school is: area = 0.5 * b * h , where b is the length of the base of the triangle, and h is the height/altitude of the triangle.
How is Heron’s formula derived?
We can derive Heron’s formula by using the Pythagoras theorem, area of a triangle formula, and algebraic identities. We construct an altitude from the top vertex to the base of the triangle, which divides the triangle into 2 triangles.
What is triangle law of vector addition Shaalaa?
Statement: “When two vectors are represented by two sides of a triangle in magnitude and direction were taken in the same order then the third side of that triangle represents in magnitude and direction the resultant of the vectors.”
What is the cross product of two vector quantities?
The cross product of two vector quantities is another vector whose magnitude varies as the angle between the two original vectors changes. The cross product is sometimes referred to as the vector product of two vectors.
Is the cross product the determinant?
Connection with the Determinant There are theoretical reasons why the cross product (as an orthogonal vector) is only available in 0, 1, 3 or 7 dimensions. However, the cross product as a single number is essentially the determinant (a signed area, volume, or hypervolume as a scalar).
What is a cross product of vectors?
The cross product a × b is defined as a vector c that is perpendicular (orthogonal) to both a and b, with a direction given by the right-hand rule and a magnitude equal to the area of the parallelogram that the vectors span.
What is Heron’s formula for area of triangle?
Heron’s formula, formula credited to Heron of Alexandria (c. 62 ce) for finding the area of a triangle in terms of the lengths of its sides. In symbols, if a, b, and c are the lengths of the sides: Area = Square root of√s(s – a)(s – b)(s – c) where s is half the perimeter, or (a + b + c)/2.
