Use the Law of Pythagoras to find the resultant vector. For the angle, you can use the arc-tangent. Or simply use the rectangular-->polar conversion, available on most scientific calculators.
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.
Yes. Here is an example: Vector A: 10 units towards the right. Vector B: 9 units towards the left. This is the same as (-9) units to the right. A + B: 10 + (-9) = +1 units to the right. In fact, the resulting vector can be made arbitrarily small, if the two vectors are similar in size and point in opposite directions (or nearly so).
Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.
Answer: There are no "pseudo vectors" there are pseudo "rules". For example the right hand rule for vector multiplication. If you slip in the left hand rule then the vector becomes a pseudo vector under the right hand rule. Answer: A pseudo vector is one that changes direction when it is reflected. This affects all vectors that represent rotations, as well as, in general, vectors that are the result of a cross product.
If the two vectors are directly opposite each other, then subtract the smaller one from the larger one and that will be your resultant force. For example, if the force downwards is 5 N and the force upwards is 2 N, the resultant force is 3 N downwards. If the one or both of the two vectors are angled, you need to replace the angled vectors with two right-angled vectors and then add those to create the resultant vectors.
When you resolve a vector, you replace it with two component vectors, usually at right angles to each other. The resultant is a single vector which has the same effect as a set of vectors. In a sense, resolution and resultant are like opposites.
The two vectors form the minor legs of a right angled triangle and the resultant is the hypotenuse of the triangle. Its magnitude, therefore, is the square root of the sum of the squared magnitudes of the two vectors.
No. Vectors add at rightangle bythe pythagoran theorem: resultant sum = square root of (vector 1 squared + vector 2 squared)
The outcome is called the resultant no matter what angle At right angles the resultant is calculated a the hypotenuse of the triangle with each vector as sides
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
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.
Yes. Any number of vectors, two or more, can result in zero, if their magnitudes and directions are just right. One vector can result in zero only if its magnitude is zero.
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Yes. Here is an example: Vector A: 10 units towards the right. Vector B: 9 units towards the left. This is the same as (-9) units to the right. A + B: 10 + (-9) = +1 units to the right. In fact, the resulting vector can be made arbitrarily small, if the two vectors are similar in size and point in opposite directions (or nearly so).
Let two equal magnitude vectors be 'X'.. Then, resultant=1.414X
Yes. This is the basis of cartesian vector notation. With cartesian coordinates, vectors in 2D are represented by two vectors, those in 3D are represented by three. Vectors are generally represented by three vectors, but even if the vector was not in an axial plane, it would be possible to represent the vector as the sum of two vectors at right angles to eachother.