for the resultant to be maximum, both the vectors must be parallel. hence the angle between them must be 0 degrees. Show What should be the angle between vectors A and B for the resultant to be minimum?The resultant of two vector is minimum when both vectors are equal and in opposite direction i.e. the angle between the vector is 180 degrees. How do you find the direction of the resultant vector? To draw the resultant vector, join the tail of the first vector with the second vector’s head and put the arrowhead. To determine the magnitude, measure the length of resultant R, and to find out the direction, measure the angle of the resultant with the x-axis. When two vectors are added together their resultant is a minimum when the angle between them is? For the magnitude of the resultant of two forces to be minimum, the angle between the two vectors that represent the forces should be 180 degrees. In other words the forces should be in the opposite direction. How do you calculate the resultant?To find the resultant force subtract the magnitude of the smaller force from the magnitude of the larger force. The direction of the resultant force is in the same direction as the larger force. A force of 5 N acts to the right, and a force of 3 N act to the left. Calculate the resultant force. What angle between two vectors is Theta?The Formula for the Angle between Two Vectors A vector is said to be in standard position if its initial point is the origin (0, 0). Where \theta is the angle between a and b vectors. Can the resultant of four vectors be zero? Can four vectors do ? If can not balance the third vector which is in a differet plane. The resultant of four coplanar vectors can be zero. if they are represented in magbitude and direction by four sides on a polygon taken in the same order. Can you find the angle between resultant and vector? Working out the sides and angles of a triangle, given a side, side and included angle is basic trig. so you don’t have to use components. But 20 million flies can’t be wrong and using components is usually the most convenient way. Can we find the angle between resultant and one of its vectors without breaking into components? What is the magnitude of the sum of two vectors?The sum of two vectors is known as the resultant vector. It is a single vector that can replace the two vectors and produce the same effect. The magnitude of the resultant of two vectors →F 1, →F 2 F 1 →, F 2 → having an angle of α α between them, is R= √F 2 1 +F 2 2 +2F 1F 2cosα R = F 1 2 + F 2 2 + 2 F 1 F 2 c o s α, where: When does the resultant have the smallest angle?The resultant is largest when the two vectors are aligned, so 0 radians would be the angle between them. The resultant is least when the two vectors are opposed, so pi radians would be the angle between them. A ball is thrown vertically upward with a velocity u from the top of a tower. How to calculate the derivation for two vectors? Give the derivation for resultant of two vectors and for the angle between resultant and a vector. Give the derivation for resultant of two vectors and for the angle between resultant and a vector.
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Answer (Detailed Solution Below) Option 3 : 180°
CONCEPT: Parallelogram law of vector addition:
Where P and Q = magnitude of the two vectors, θ = angle between P and Q CALCULATION:
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Video Lessons & PDF Notes Trusted by 2,95,76,072+ Students Suppose two vectors P and Q are acting simultaneously at a point making an angle α. Now according to parallelogram law the magnitude of the resultant. R = √(P2 + Q2 + 2PQ cosα) From the above equation it is evident that R depends on the angle between P and Q i.e., on α.  Minimum value of the resultant: The magnitude of R will be minimum when cos α is minimum i.e., cos α = – 1 = cos 180° or, α = 180°. R(minimum) = √(P2 + Q2 + 2PQ cos 1800) = √(P2 + Q2 ~ 2PQ) = (P ~ Q) Thus, when two vectors act along the same line but in opposite direction, the magnitude of the resultant will be minimum. In other words, the minimum value of magnitude of the resultant of the two vectors cannot be less than their subtraction. (Here, ~ sign between P and Q means that the larger one should be written first e.g., suppose Q > P, then P ~ Q = Q – P) If two equal and opposite forces act along the ends of a straight line, the resultant will be zero. You Might Also Like |
The resultant of two vectors will be minimum, if they are
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