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How will you get the third vector if the 1st and 2nd vector was given and the resultant vector is equal to 0?
Wiki User
∙ 14y ago
by method of finding resultant
Wiki User
∙ 14y ago
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Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
What is the resultant of two vectors?
The resultant of two vectors is a third vector., for example V1 + V2 = V3. V3 may be equal to zero, greater than zero or less than zero.
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.
How will you get the resultant of all vectors?
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
How do you prove three vectors are equal to zero?
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
Can the resultant of two vectors of the same magnitude be equal to the magnitude of either of the vector proof mathematically?
Yes. If the two vectors are two sides of an equilateral triangle, then the resultant is the third side and therefore equal in magnitude.
What is the resultant of two vectors?
The resultant of two vectors is a third vector., for example V1 + V2 = V3. V3 may be equal to zero, greater than zero or less than zero.
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.
How will you get the resultant of all vectors?
Graphical Vector AdditionDraw your first vector. Then draw the tail (start) of your second vector at the tip (end) of your first vector. Then draw the tail of your third vector at the tip of you third vector (if it exists,) and so on. To find the resultant, draw a vector from the tail of the first vector to the tip of the last vector. The angle of the resultant will be between the resultant's tail and the first vector's tail. To find these values, it is recommended that you use a scale (e.g. 1cm:1m) and a protractor so that your values are accurate.Or, to do it mathematically (with 2 vectors):You have vector a with angle Ao, and vector b with angle Bo.To get vector c (resultant,) break the vectors up into their x and y components, then add the x and y components to find the x and y of the resultant. To find the magnitude of vector c, use Pythagoras's theorem, a2 + b2 = c2. To find the angle of c, use inverse tangent, tan-1(y/x)Example:Remember that sin = y and cos = x. Thus, to find the x component of a vector, use cos, and to find the y component of a vector, use sin.c = square root( (acosA + bcosB)2 + (asinA + bsinB)2 )angle of c = tan-1( (asinA + bsinB)/(bcosA + bcosB) )
What are the ways of determining the resultant vector?
You can do it graphically by drawing the vectors with the end of the first touching the beginning of the second, the end of the second touching the beginning of the third, and so on, being careful to maintain the direction and the scale of the magnitude of each. The resultant is then the vector that starts at the beginning of the first vector and ends at the end of the last vector. You should get the same resultant no matter what order you put the vectors in. You can do it matematically by trigonometrically separating each vector into its x and y components, adding together all the x's and adding together all the y's, then calculating the resultant. Think of each vector as the hypotenuse of a right triangle. After adding together the x's and y's, the two sums are the two sides of a right triangle whose hypotenuse is the resultant.
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.
Under what circumstances can a vector have components that are equal in magnitude?
(Magnitude of the vector)2 = sum of the squares of the component magnituides Let's say the components are 'A' and 'B', and the magnitude of the vector is 'C'. Then C2 = A2 + B2 You have said that C = A, so C2 = C2 + B2 B2 = 0 B = 0 The other component is zero.
State and explain triangle law of vector?
if two vectors are represented in magnitude and direction by the two sides of a triangle taken in one order ,their resultant vector is represented by the third side of the triangles taken in reverse order
What is meant by rectangular triangle componenets of a vector?
If you plotted the original path and velocity, and the path and velocity of the 'impacting' force, then the third leg of the triangle will be the resultant path and velocity.
What is triangle law in vectors?
A law which states that if a body is acted upon by two vectors represented by two sides of a triangle taken in order, the resultant vector is represented by the third side of the triangle.
How do you prove three vectors are equal to zero?
If the sum of their components in any two orthogonal directions is zero, the resultant is zero. Alternatively, show that the resultant of any two vectors has the same magnitude but opposite direction to the third.
How do you find the y-component of a vector if you are given x-component and z-component?
You don't. Knowing two of the vector's orthogonal components doesn't tell you what the third one is. It could be absolutely anything.
