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If you have vectors U = (ai + bj + ck) and V = (di + ej + fk) and x is the angle between them, then
cos(x) = U.V/(|U|*|V|)
= (ad + be + cf)/[sqrt(a2+b2+c2)*sqrt(d2+e2+f2)]
The angle x can be determined by calculating arccos of the above value.
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∙ 9y ago
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What is the angle between two vectors if their sum is to be maximum?
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
How do you find angle between vectors?
To find the angle between two vectors, you need to use this form: a ∙ b / (|ab|) = cos(θ) θ = arccos(a ∙ b / (|ab|)) where a and b are vectors. Compute the dot product and the norm of |a| and |b|. Then, compute the angle between the vectors.
When are vectors said to be perpendicular?
Perpendicular means that the angle between the two vectors is 90 degrees - a right angle. If you have the vectors as components, just take the dot product - if the dot product is zero, that means either that the vectors are perpendicular, or that one of the vectors has a magnitude of zero.
The sum of two vectors is a minimum when the angle between them is what?
180 degrees. Then the sum of the two vectors has a magnitude equal to the difference of their individual magnitudes.
How many radians equal to 540 angle?
180 deg = π radians so 540 deg = 3π radians.
What is the angle between two vectors if their sum is to be maximum?
The resultant vector has maximum magnitude if the vectors act in concert. That is, if the angle between them is 0 radians (or degrees). The magnitude of the resultant is the sum of the magnitudes of the vectors.For two vectors, the resultant is a minimum if the vectors act in opposition, that is the angle between them is pi radians (180 degrees). In this case the resultant has a magnitude that is equal to the difference between the two vectors' magnitudes, and it acts in the direction of the larger vector.At all other angles, the resultant vector has intermediate magnitudes.
When does the magnitude of dot product and cross product of vectors is equal?
If x is the angle between the two vectors then the magnitudes are equal if cos(x) = sin(x). That is, when x = pi/4 radians.
What should be the angle between 2 vectors a?
The angle between 2 vectors can have any value.
Can the scaler product of two vectors be negetiv if the answer is yes provid a proof and given exampl?
Yes, for example the vectors <1, 0> and <-1, 0>. In general, if the angle between the two vectors is more than 90 degrees (or pi/2 radians), the scalar product is negative.
How do you find angle between vectors?
To find the angle between two vectors, you need to use this form: a ∙ b / (|ab|) = cos(θ) θ = arccos(a ∙ b / (|ab|)) where a and b are vectors. Compute the dot product and the norm of |a| and |b|. Then, compute the angle between the vectors.
What is the difference between a zero angle and a straight angle?
A straight angle is pi radians (180 degrees) so the difference is pi radians.
When the angle between two vectors is equal to zero?
When the angle between two vectors is zero ... i.e. the vectors are parallel ... their sum is a vector in thesame direction, and with magnitude equal to the sum of the magnitudes of the two original vectors.
When two vectors are added and their magnitude is equal to the magnitude of resultan what will be angle in between them?
if you add the vectors magnitude and equal to resultant the angle between them is 0
What is the angle 135 in radians?
There are 2.356 radians in 135 degrees of angle.
Why straight angle is not reflex angle?
A straight angle is pi radians (180 degrees). A reflex angle is more than pi radian but less than 2*pi radians (between 180 and 360 degrees).
What is the mesurement of a reflex angle?
the measurement of a reflex angle is between 180 and 360 degrees, or between pi and 2pi in radians.
Application of relation between arc of length and central angle?
The relation between the arc of length and the central angle is that the arc of length divided by one of the sides is the central angle in radians. If the arc is a full circle, then the central angle is 2pi radians or 360 degrees.
