Take any three vectors in a plane which, when placed end-to-end form a triangle. The resultant of the three vectors will be zero.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
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.
Yes if you put them "head to tail" and the head of the fourth one points to the tail of the first one the resultant is zero.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
No. For three vectors they must all lie in the same plane. Consider 2 vectors first. For them to resolve to zero, they must be in opposite direction and equal magnitude. So they will lie along the same line. For 3 vectors: take two of them. Any two vectors will lie in the same plane, and their resultant vector will also lie in that plane. Find the resultant of the first two vectors, and the third vector must be along the same line (equal magnitude, opposite direction), in order to result to zero. Since the third vector is along the same line as the resultant vector of the first two, then it must be in the same plane as the resultant of the first two. Therefore it lies in the same plane as the first two.
No. The tenth vector would have to be matched by one equal and opposite vector to yield a zero resultant, or by multiple vectors in the second plain collectively yielding a zero resultant for that plane. It would be possible, for example, for 8 vectors to be on the same plane and two on a different plane to give a zero resultant.
Yes, three vectors that do not lie in the same plane can give a zero resultant if they form a closed triangle. This can happen when the vectors cancel each other out due to their directions and magnitudes.
yes the resultant of the two vectors can be zero.it can be illustrated by drawing following diagram.a triangle may be considered as a vector diagram in which the force polygon close and the resultant of the three vectors is zero.
To find the magnitude and direction of the resultant vector, you can use the parallelogram law of vector addition. Add the two vectors together to form a parallelogram, then the diagonal of the parallelogram represents the resultant vector. The magnitude can be calculated using trigonometry, and the direction can be determined using angles or components.
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.
The wind is blowing at a vector of 225 degrees with a magnitude of 75. The original heading is on a vector of zero with a magnitude of 2500. The resultant vector is then 15 degrees east of north at 203.98 kmh.
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.
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.
Yes if you put them "head to tail" and the head of the fourth one points to the tail of the first one the resultant is zero.
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.