Table of Contents
- 1 What is the angle between two unit vectors?
- 2 Are all vectors right angles?
- 3 What should be the angle between two vectors for the magnitude of their resultant to be maximum?
- 4 When two vectors that are at an angle other than 90 to each other are added which mathematical techniques can be used to find the resultant vector?
- 5 How do you find the magnitude of 3 unit vectors at 90°?
- 6 What is the formula for finding cosine of angle between two vectors?
What is the angle between two unit vectors?
“Angle between two vectors is the shortest angle at which any of the two vectors is rotated about the other vector such that both of the vectors have the same direction.”
What should be the angle between two vectors if their resultant is 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.
Are all vectors right angles?
With all vectors being at right angles to one another, their addition leads to a resultant that is at the hypotenuse of a right triangle. The Pythagorean theorem can then be used to determine the magnitude of the resultant….
| Vector | East-West Component | North-South Component |
|---|---|---|
| Resultant A to G | 360 m, East | 40 m, North |
What should be the angle between two vectors of equal magnitude so that their vector sum is equal to one of them only *?
120°
θ be the angle between both the vectors. Both the vectors have the same magnitude. Let the resultant have magnitude equal to vector A. Hence, the angle between the two vectors is 120°.
What should be the angle between two vectors for the magnitude of their resultant to be maximum?
for the resultant to be maximum, both the vectors must be parallel. hence the angle between them must be 0 degrees.
What should be the angle between two vectors A and B for their resultant RI to be maximum II?
The angle should be 180 degrees for the resultant R to be minimum. The angle should be 180 degrees for the resultant R to be minimum.
When two vectors that are at an angle other than 90 to each other are added which mathematical techniques can be used to find the resultant vector?
The Pythagorean theorem
The Pythagorean theorem is a useful method for determining the result of adding two (and only two) vectors that make a right angle to each other.
What is the angle between the two vectors?
Their resultant is given by A+B.Its given that the magnitude of the resultant is also 1. So the angle between the vectors should be 120 degrees. Note that an angle of 240 degree between the two vectors is equivalent to an angle of 120 degree. So there is only one possible angle and that is 120 degree
How do you find the magnitude of 3 unit vectors at 90°?
You simply use the value √2 for two unit vectors at 90°. Just to save your time we avoid going through calculations everytime. Similarly Magnitude of 3 unit vectors is √3 (√ (i)² + (j)²+ (k)²). However the angle between them in such a case can be calculated be Direction Cosines. 8 clever moves when you have $1,000 in the bank.
What is the axis of a zero and 180 degree vector?
In the zero case the axis does not matter and can be anything because there is no rotation round it. In the 180 degree case the axis can be anything at 90 degrees to the vectors so there is a whole range of possible axies. One approach might be to define a quaternion which, when multiplied by a vector, rotates it:
What is the formula for finding cosine of angle between two vectors?
The formula for finding cosine of angle between two vectors can be deduced by the formula of angle between two vectors and is So, the cosine of the angle between two vectors can be calculated by dividing the dot product of the vectors by-product of their magnitudes.