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If the three vectors a b and c are coplanar then the missed product a x b. c is?
Wiki User
∙ 6y ago
Not sure what you mean by "missed" but the answer is 0.
Wiki User
∙ 6y ago
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What is the algebraic definition of a cross product?
Cross product also known as vector product can best be described as a binary operation on two vectors in a three-dimensional space. The created vector is perpendicular to both of the multiplied vectors.
Cross product is not difine in two space why?
When performing the cross product of two vectors (vector A and vector B), one of the properites of the resultant vector C is that it is perpendicular to both vectors A & B. In two dimensional space, this is not possible, because the resultant vector will be perpendicular to the plane that A & B reside in. Using the (i,j,k) unit vector notation, you could add a 0*k to each vector when doing the cross product, and the resultant vector will have zeros for the i & jcomponents, and only have k components.Two vectors define a plane, and their cross product is always a vector along the normal to that plane, so the three vectors cannot lie in a 2D space which is a plane.
What are the properties of a dot product?
In mathematics, the dot product is an algebraic operation that takes two equal-length sequences of numbers (usually vectors) and returns a single number obtained by multiplying corresponding entries and adding up those products. The name is derived from the interpunct "●" that is often used to designate this operation; the alternative name scalar product emphasizes the scalar result, rather than a vector result.The principal use of this product is the inner product in a Euclidean vector space: when two vectors are expressed in an Orthonormal basis, the dot product of their coordinate vectors gives their inner product. For this geometric interpretation, scalars must be taken to be Real. The dot product can be defined in a more general field, for instance the complex number field, but many properties would be different. In three dimensional space, the dot product contrasts with the cross product, which produces a vector as result.
If three points are coplanar then are they collinear?
Not necessarily. Coplanar means that points lie on the same plane whereas collinear means that points lie on the same line. Points on a plane do not necessarily lie along the same line.
Can three parallel vectors of uneven magnitude add to zero?
Yes - if you accept vectors pointing in opposite directions as "parallel". Example: 3 + 2 + (-5) = 0
If the three vectors a b and c are coplanar then the missed product a x b c is?
zero
How do you show that that the three vectors are coplanar?
Three vectors are coplanar if they sum to zero. V1 + V2 + V3 = o means the three vectors are coplanar.
Can three vectors add up to zero if they are not coplanar?
yes
What is the difference between coplanar vectors and collinear vectors?
The term collinear is used to describe vectors which are scalar multiples of one another (they are parallel; can have different magnitudes in the same or opposite direction). The term coplanar is used to describe vectors in at least 3-space. Coplanar vectors are three or more vectors that lie in the same plane (any 2-D flat surface).
What is the condition for being 3 vectors in a plane?
The general idea is that 3 vectors are in a plane iff they are not linearly independent. This can be checked in several ways:guessing a way to represent one of them as a linear combination of the other two - if it can be done, then they are coplanar;if they are three-dimensional, simply by calculating the determinant of the matrix whose columns are the vectors - if it's zero, they are coplanar, otherwise, they aren't;otherwise, you may calculate the determinant of their gramian matrix, that is, a matrix whose ij-th entry is the dot product if the i-th and j-th of the three vectors (e.g. it's 1-2-nd entry would be the dot product of first and second of them); they are coplanar iff the determinant is zero.
How can four non coplanar vectors give a resultant zero?
Easy, the fourth vector (D) be opposite the sum of the other three non-coplanar vectors (A , B, C). 0=A + B + C + D where D = -(A + B + C).
He vector sum of three vectors gives a zero resultant what can be orientation of the vectors?
The orientation of the three vectors that sum to zero must be coplanar, contained in the same common plane, including being contained in a common line in a plane.
What is non-coplaner vectors?
They are a pair of vectors which are not parallel but whose lines of action cannot meet.
Under what condition the sum of three vectors will be zero?
Three vectors sum to zero under the condition that they are coplanar (lie in a common plane) and form a triangle. If the vectors are not coplanar, they will not sum to zero. Another way of looking at it is that the sum is zero if any vector is exactly equal in magnitude and opposite in direction to the vector sum (so-called resultant) of the remaining two.
If Three vectors are co-planner then there product is?
Zero
What are the operation on vector?
That really depends on the type of vectors. Operations on regular vectors in three-dimensional space include addition, subtraction, scalar product, dot product, cross product.
Can three coinitial vectors be non coplanar?
Of course. Take a moment and look at the corner of your room, where two wallsand the floor meet. Take a crayon and draw three line segments from the cornerpoint, one on each wall and one on the floor. There you have the vectors thatyou've described.
