The magnitude of the vector from P = (x1, y1, z1) to Q = (x2, y2, z2)
is sqrt[(x2 - x1)2 + (y2- y1)2 + (z2 - z1)2]
(Pythagoras in 3-D).
The magnitude of a vector can be found by taking the square root of each of the vector components squared. For example, if you had the vector 3i+4j, to find the magnitude, you take sqrt ( 3²+4² ) To get: sqrt ( 9+16 ) sqrt ( 25 ) = 5 Works the same in 3D or more, just put all the vector components in.
You need to take the magnitude of the cross-product of two position vectors. For example, if you had points A, B, C, and D, you could take the cross product of AB and BC, and then take the magnitude of the resultant vector.
No. If the vector is 2D then it's magnitude is (x^2+y^2)^0.5 where x and y are the components and ^0.5 means take the square root. In 3D this becomes (x^2+y^2+z^2)^0.5 etc. Thus the magnitude is always at least as big as one of the components. Here's an example of a 3D vector: (3,4,5) |(3,4,5)|=(3^2+4^2+5^2)^0.5=(9+16+25)^0.5=50^0.5=7.07... If y and z were 0: (3,0,0) |(3,0,0)|=(3^2+0^2+0^2)^0.5=(9+0+0)^0.5=9^0.5=3 ie the magnitude is the same size as x. You can also consider this geometrically. A vector is an arrow and the magnitude represents the length of the arrow. Vector addition is the 'adding' of these arrows so (3,4,5)=(3,0,0)+(0,4,0)+(0,0,5). Clearly the length of an arrow built of three smaller ones can't be less than any one of them.
here are the possible answers: A) A tridimensional vector B) A 4D vector C) A 5D vector D) An scalar number E) It is undefined
A vector can be resolved into infinitely many sets of components in both 2D and 3D space.
The magnitude of a vector can be found by taking the square root of each of the vector components squared. For example, if you had the vector 3i+4j, to find the magnitude, you take sqrt ( 3²+4² ) To get: sqrt ( 9+16 ) sqrt ( 25 ) = 5 Works the same in 3D or more, just put all the vector components in.
Because speed is the magnitude of the velocity vector. The velocity consists of the speed and the direction, and the whole thing can be embodied in a 3D vector. If you like the velocity is the magnitude (the speed), which is a scalar (just a real number), multiplied by a unit vector in the right direction.
Yes, it is a vector quantity.
It is -4d.
You need to take the magnitude of the cross-product of two position vectors. For example, if you had points A, B, C, and D, you could take the cross product of AB and BC, and then take the magnitude of the resultant vector.
No. If the vector is 2D then it's magnitude is (x^2+y^2)^0.5 where x and y are the components and ^0.5 means take the square root. In 3D this becomes (x^2+y^2+z^2)^0.5 etc. Thus the magnitude is always at least as big as one of the components. Here's an example of a 3D vector: (3,4,5) |(3,4,5)|=(3^2+4^2+5^2)^0.5=(9+16+25)^0.5=50^0.5=7.07... If y and z were 0: (3,0,0) |(3,0,0)|=(3^2+0^2+0^2)^0.5=(9+0+0)^0.5=9^0.5=3 ie the magnitude is the same size as x. You can also consider this geometrically. A vector is an arrow and the magnitude represents the length of the arrow. Vector addition is the 'adding' of these arrows so (3,4,5)=(3,0,0)+(0,4,0)+(0,0,5). Clearly the length of an arrow built of three smaller ones can't be less than any one of them.
3 :)
here are the possible answers: A) A tridimensional vector B) A 4D vector C) A 5D vector D) An scalar number E) It is undefined
A vector can be resolved into infinitely many sets of components in both 2D and 3D space.
Generating 3D textures is called rendering or vector mapping.
A line (2D), ray (2D), vector (2D), line segment (2D), a mobius strip (3D), or a klein bottle (3D).
The usual way to do this is to express each vector as the sum of two or three perpendicular vectors (two in a plane, three in 3D space). Then you can add the components of the two vectors, to get the new vector.For the case of two dimensions, on most scientific calculators there is a neat feature called rectangular-to-polar and polar-to-rectangular conversion, which can quickly convert a vector from polar (i.e., magnitude and angle) to rectangular (i.e., x-coordinate and y-coordinate), or vice versa.