Explain scalar multiple of vector?
- acafrao341Lv 51 decade agoFavorite Answer
Geometrically, if you think of a vector as an arrow, a scalar multiple is an arrow pointing in the same direction, but having a different length.
If you think of a vector algebraically, as an ordered list of numbers, a scalar multiple is the vector where each component is multiplied by some constant:
a(x, y, z) = (ax, ay, az)
Hope this helps,
- EvelynLv 44 years ago
A scalar only has a size... and it can have a unit of measurement. For exactly, 50 kg is a scalar, and 25 kmh is a scalar. A vector is a scalar with a direction attached, so (since weight can be converted to Newtons), 490 N (down) is a vector... 25kmh (east) is a vector.
- MaryLv 44 years ago
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A scalar is simply a number. For example, the speed at which your car is moving is a scalar value. A vector is a one-dimensional array (or list) of scalars. In the simplest case, you will have two scalars comprising a vector. For example "(1,0)" is a one-dimensional array with two scalars that forms a vector. The easiest way to visualize this is to think of the numbers as coordinates on a graph. Imagine the first number as the distance one travels along the x-axis and the second number as the distance one travels along the y-axis. So for (1,0) we would draw an arrow from the origin (0,0) to (1,0), signifying that we are moving one unit along the x-axis. A "unit vector" is a vector that is exactly one unit in length. You can turn any vector into a unit vector by dividing its x and y components by the vector's magnitude. Unit vectors are very useful in mathematics, engineering, and 3-D computer graphics. Velocity is a good example of a quantity that can be represented by a vector. Velocity has both a direction and a speed. Pretend you are in a very small car located at the origin of your graph paper and headed in a northeast direction at 10 miles per hour. The speed (which is a scalar -- just a number) is obviously 10 mph, but we must also represent the direction, and to do that we would draw a line segment from the origin heading 45 degrees to the upper-right and 10 units in length. Now looking at how far that line segment extends on the x-axis and the y-axis, we can determine what vector represents the car's velocity. In this case, the vector would be (7.07,7.07) -- that is, if you drove 10 miles per hour in a northeast direction for an hour, you would find that you were 7.07 miles north and 7.07 miles east of where you started from. A vector can have as many dimensions as you want. What I described above was a two-dimensional vector (i.e., it only has an x and a y component), but you can also have three-dimensional vectors, four-dimensional vectors, and so forth. The number of scalars making up the vector determines its dimension. Scalars and vectors have many uses, especially in physics. Scalars are used for anything that can be represented by a single value. Vectors are used to measure anything that requires multiple values in order to be represented. For example, in physics a force is represented by a vector; it has both a magnitude and a direction. By representing forces as vectors, it becomes easy to see how how multiple forces acting on an object from different directions will add together; you just add each respective component to get the result. Both "scalars" and "vectors" are fundamental concepts in mathematics, physics, and engineering. Once you master them, the next (big) step is to learn about _tensors_, which are far more complex and far more powerful.
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- 1 decade ago
scalar multiplication of vectors is just like scalar multiplication of regular numbers. i like to think of it as distribution, but hey, i didnt make up the term. lets say you are given the problem::
6<1, 3, 5>
that turns out to be
<6x1, 6x3, 6x5>
which equals <6, 18, 30>
scalar multiplication changes the magnitude of the vector but NOT the direction.
Hope everyones answers helps.
- uncle JLv 41 decade ago
A vector has both magnitude and direction. scalar multiplication changes the magnitude but not direction