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How can you add three vectors of equal magnitude in a plane such as their resultant is zero?
Wiki User
∙ 11y ago
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.
Wiki User
∙ 11y ago
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Can three vectors of equal magnitude be combined to give a zero resultant?
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
Can three vectors not in one plane give zero resultant?
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.
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.
Can 4 vectors not in a plane give zero resultant?
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.
What is the difference between coplanar and non-coplanar vectors?
Coplanar :The vectors are in the same plane.Non coplanar :The vectors are not in the same plane.
Can three vectors of equal magnitude be combined to give a zero resultant?
Yes, put the three vectors in a plane, with a separation of 120 degrees between each vector and each of the other vectors.
Can three vectors not in one plane give zero resultant?
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.
Ten vectors together add to give a zero resultant it is possible that nine of these vectors are on the same plane but the tenth is not on this plane?
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.
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.
Can three vectors lying in plane give zero resultant?
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.
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.
Can 4 vectors not in a plane give zero resultant?
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.
A plane can travel with a speed of 80 mi-hr with respect to the air determine the resultant velocity of the plane magnitude only if it encounters a 10 mi-hr headwind?
sol:- resultant velocity of a plane=80-10 =70m/s
When two vectors are acting at a point along different directions how do we determine magnitude and direction of the resultant?
The usual way to do this is to express each vector as the sum of two or three perpendicular vectors (two in a plane, three in 3D space). Then you can add the components of the two vectors, to get the new vector.For the case of two dimensions, on most scientific calculators there is a neat feature called rectangular-to-polar and polar-to-rectangular conversion, which can quickly convert a vector from polar (i.e., magnitude and angle) to rectangular (i.e., x-coordinate and y-coordinate), or vice versa.
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.
If the resultant of three vectors is zero they must be will in the same plane?
Not necessarily. Suppose you have three vectors (ax + by + cz), (gx + hy +iz) and (mx + ny + oz) then as long as a+g+m = b+h+n = c+i+o = 0 the resultant is zero.
A novice pilot sets a plane's controls thinking the plane will fly at 2.5 X 102 kmh to the north if the wind blows at 75 kmh toward the southeast what is the plane's resultant velocity?
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.
