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What is Linearly independent Vectors?
Linearly independent vectors are a set of vectors in which no vector can be expressed as a linear combination of the others. This means that the only solution to the equation formed by setting a linear combination of these vectors to zero is that all coefficients must be zero. In other words, if you have a collection of linearly independent vectors, removing any one of them would alter the span of the set. This concept is fundamental in linear algebra, particularly in determining the dimensionality of vector spaces.
What does the cross product of two vectors represent in mathematics?
The cross product of two vectors in mathematics represents a new vector that is perpendicular to both of the original vectors. It is used to calculate the area of a parallelogram formed by the two original vectors and to determine the direction of a resulting force in physics.
How do you find the area of triangle formed by vectors?
To find the area of a triangle formed by two vectors (\mathbf{a}) and (\mathbf{b}), you can use the formula: [ \text{Area} = \frac{1}{2} |\mathbf{a} \times \mathbf{b}| ] Here, (\mathbf{a} \times \mathbf{b}) represents the cross product of the two vectors, and (|\cdot|) denotes the magnitude of that vector. The area is half the magnitude of the cross product since the cross product gives the area of the parallelogram formed by the two vectors.
How many vectors can be formed by joining the vertices of a given quadrilateral?
12 vectors, unless it is a parallelogram (13 if you include the null vector). If the quadrilateral is a parallelogram there will be two fewer.
If a set of vectors is laid head to tail and formed a closed polygon is the resultant zero?
yes it is
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 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.
Party formed to fight the spread of slavery?
Independent
What alliance was formed after the former USS.R dissolved?
A common wealth of independent states.
In 1968 George Wallace formed the?
American Independent Party
What alliance was formed after the USSR dissolved?
commonwealth of independent states.
District formed by dividing a small independent kingdom?
Shire
