zero
Three vectors are coplanar if they sum to zero. V1 + V2 + V3 = o means the three vectors are coplanar.
yes
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.
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).
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.
Not sure what you mean by "missed" but the answer is 0.
Three vectors are coplanar if they sum to zero. V1 + V2 + V3 = o means the three vectors are coplanar.
yes
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).
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.
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).
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.
They are a pair of vectors which are not parallel but whose lines of action cannot meet.
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.
Zero
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.
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.