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In order for two vectors to add up to zero:
-- their directions must be exactly opposite
-- their magnitudes must be exactly equal
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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.
What is the term for vectors that lie in a straight line?
One-dimensional
What is collinear vector and examples?
vectors that have same direction and lie on same plane .example a person sitting in an aeroplane or helicopter, a person on a sale boat.
Where would a point lie if its ordinate is 0?
If the point's ordinate, or y-coordinate, is zero then it must lie on the x-axis somewhere.
If vector A is perpendicular to vector B and C then Vector A is parallel to?
Vector A is parallel to the cross product of vectors B and C, and it is parallel to the axis that neither B or C lie along if the two other axes are defined as the axes that B and C lie along.
Can three vectors not lying in plane give 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.
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?
Yes, it is possible for nine vectors to lie in the same plane while the tenth vector is not on that plane. This situation can occur when the vectors in the plane add up to a resultant that cancels out or balances the out-of-plane vector, resulting in a zero net sum.
What is the minimum number of vectors having different planes which can be added to give zero resultant?
you'll need at least three. Think of them as being connected. To have a zero resultant, putting the vectors together head to tail should form a closed shape. The first vector can be in any direction. The second vector starts where the first ended, and extends in a different plane. The last vector starts from where the second ended and extends to the beginning of the first vector. The three end up making a triangle, which gives you a zero resultant
Under what condition the sum of three vectors will be zero?
The sum of three vectors will be zero if they can form a closed triangle when arranged tip-to-tail. This means the vectors must have magnitudes and directions that cancel each other out to form a closed loop with no resultant vector.
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 is non-coplaner vectors?
They are a pair of vectors which are not parallel but whose lines of action cannot meet.
What is the term for vectors that don't lie in a straight line but instead point in different directions?
The term for vectors that don't lie in a straight line but point in different directions is "non-collinear vectors."
What is the term given to vectors that don't lie in a straight line but point in different directions?
Displacement Vectors
What is the term given to vectors that dont lie in a straight line but instead point in different directions?
The term for vectors pointing in different directions is called linearly independent vectors. These vectors do not lie on the same line or plane, and they provide unique information to describe a space.
What is the term for vectors that lie in a straight line?
One-dimensional
What are coplaner vectors?
Coplaner means all points, lines, circles, vectors etc. lie in a single (usually theoretical) flat plane.
