0
Yes - if you accept vectors pointing in opposite directions as "parallel". Example:
3 + 2 + (-5) = 0
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What is the resultant of a 3 unit vector and 4 unit vector at right angles to each other?
The multiplicative resultant is a three unit vector composed of a vector parallel to the 3 unit vector and a vector parallel to the product of the 3 unit and 4 unit vectors. R = (w4 + v4)(0 +v3) = (w40 - v4.v3) + (w4v3 + 0v4 + v4xv3) R = (0 - 0) + w4v3 + v4xv3 as v4.v3 =0 ( right angles or perpendicular)
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.
If the three vectors a b and c are coplanar then the missed product a x b. c is?
Not sure what you mean by "missed" but the answer is 0.
What is the largest possible number of parallel sides in a hexagon?
Providing that it is a regular 6 sided hexagon then it will have 3 pairs of opposite parallel sides. Though an irregular hexagon (shaped as the outline of an L) can have 2 sets of three parallel sides.
What is the physical meaning of determinant of a matrix?
for a 3x3 matrix, it can be interpreted as the volume of the hexahedron formed by three vectors (each row of the matrix as one vector).
Is it is possible to add three vectors of equal magnitude and get zero?
Yes. Vectors contain both magnitude and direction. Graphically three vectors of equal magnitude added together with a zero sum would be an equilateral triangle.
Can three vectors of different magnitude be combined to give a zero resultant and can three vectors?
Yes.
Is it possible to combine two vectors of different magnitude to give a zero resultant if not can three vectors be combine?
Two vectors: no. Three vectors: yes.
Can two vectors having different magnitude be compined to give a zero resultant can three vector?
Two vectors, no; three vectors yes.
Can two vectors having different magnitude be combined to give a zero resultantis it possible for three vectors?
-- The minimum magnitude that can result from the combination of two vectors is the difference between their magnitudes. If their magnitudes are different, then they can't combine to produce zero. -- But three or more vectors with different magnitudes can combine to produce a zero magnitude.
How can you add three vectors of equal magnitude in a plane such as their resultant is zero?
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.
What circumstances will three vectors be equal in magnitude?
If they all have the same norm.
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 of equal magnitudes be added to give a vector of same magnitude and how?
Only if the magnitude of all three vectors equals 0.Suppose three vectors (xi), (xj), (xz) are added. If the above statement is true then adding these three vectors should give a magnitude of x(x2 + x2 + x2)1/2 = xSquaring both sidesx2 + x2 + x2 = x22x2=0The above expression is only solvable for x = 0Hence the answer to the above equation is no, unless both vectors are the zero vector.
Is it possible to add three vectors of equal-magnitude but different direction to get zero vector?
Yes, if the three vectors are starting from the same point and are directed at 120 degrees between each two vectors.
Why are velocity and acceleration both vectors?
They aren't, but they can be described as vectors. The most common way is to describe them as vectors of three components in Euclidian space.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vectors?
Magnitude? Yes. Simple answer: think of it as a triangle. Can a triangle have three sides of the same length? Yes. Long answer: there really isn't a long answer. To get the resultant of two vectors, one would add up the components of each vector. While it is impossible to add two vectors of the same magnitude and derive a resultant of the same magnitude AND DIRECTION as one of the vectors, one need only to create a directional difference of exactly 60 degrees between the first two vectors to result in a resultant of like magnitude. Math really is the most perfect language. Vectors are to triangles what optics are to to the study of conics!
