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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.
How do you add Vectors By rectangular components?
INTRODUCTIONRectangular component method of addition of vectors is the most simplest method to add a number of vectors acting in different directions.DETAILS OF METHODConsider two vectors making angles q1 and q2 with +ve x-axis respectively.STEP #01Resolve vector into two rectangular components and .Magnitude of these components are:andSTEP #02Resolve vector into two rectangular components and .Magnitude of these components are:andFor latest information , free computer courses and high impact notes visit : www.citycollegiate.comSTEP #03Now move vector parallel to itself so that its initial point (tail) lies on the terminal point (head) of vector as shown in the diagram.Representative lines of and are OA and OB respectively.Join O and B which is equal to resultant vector of and STEP #04Resultant vector along X-axis can be determined as:STEP # 05Resultant vector along Y-axis can be determined as:STEP # 06Now we will determine the magnitude of resultant vector.In the right angled triangle DBOD:HYP2 = BASE2 + PERP2STEP # 07Finally the direction of resultant vector will be determined.Again in the right angled triangle DBOD:Where q is the angle that the resultant vector makes with the positive X-axis.In this way we can add a number of vectors in a very easy manner.This method is known as ADDITION OF VECTORS BY RECTANGULAR COMPONENTS METHOD. For latest information , free computer courses and high impact notes visit : www.citycollegiate.com
What is the physical significance of null vectors?
Zero vector or null vector is a vector which has zero magnitude and an arbitrary direction. It is represented by . If a vector is multiplied by zero, the result is a zero vector. It is important to note that we cannot take the above result to be a number, the result has to be a vector and here lies the importance of the zero or null vector. The physical meaning of can be understood from the following examples. The position vector of the origin of the coordinate axes is a zero vector. The displacement of a stationary particle from time t to time tl is zero. The displacement of a ball thrown up and received back by the thrower is a zero vector. The velocity vector of a stationary body is a zero vector. The acceleration vector of a body in uniform motion is a zero vector. When a zero vector is added to another vector , the result is the vector only. Similarly, when a zero vector is subtracted from a vector , the result is the vector . When a zero vector is multiplied by a non-zero scalar, the result is a zero vector.
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.
How do you prove using a diagram that the magnitude of the sum of two vectors is less than or equal to the sum of the magnitude of the two vectors?
You could draw a circle [center at origin] with radius of (a + b), for the two magnitudes a and b. This represents the sum of the magnitudes. Then draw one of the vectors starting at the origin [suppose it's vector a], and then draw a circle centered at the endpoint of vector a, with a radius of b. Drawing a circle demonstrates how the second vector can point in any direction relative to the first vector. The distance from the origin to a point on this second circle is the magnitude of the resultant vector. Graphically this second circle will be entirely inside the first circle and touching it at just one point. Since it lies within the first circle, the distance from the origin to a point on that circle will be less than or equal to the radius of the first circle.
How should you correcet your lies?
By admitting what you have done and apologizing.
Is there any direction associated with the dot product of two vectors?
No. The dot product is also called the scalar product and therein lies the clue.
Vector A lies in xy planeFor what orientation will both of its rectangular components be negative?
South West orientation makes both components negative.
Vector A lies in the xy plane.For what orientation will both of its rectangular components be negative?
South West orientation makes both components negative.
Congressional witness lies under oath what has he done?
Purgery
How beauty lies in the beauty parlours?
SPA can be done like the skin
What can be done when a person lies in probate court to grant guardianship?
can order be contested
