If three vectors along co ordinate axes represent the adjacent sides of a cube of length b ,then the unit vector along its diagonal passing through the origin will be ?
Answers
Answer:
Explanation:
The diagonal of this cube is [b//b//b], so any vector along the diagonal will be a multiple of this. In particular, normalizing a diagonal vector to unity yields [1/3√//1/3√//1/3√].
A side note: in maths, vectors always pass through the origin. Well, actually they always originate at the origin. The methods for vector sum and difference that are taught in high school physics where you move arrows around the plane are conceptually correct (it can be shown that they give the correct result) but, I fear, very misleading.
In maths, there are no such things as “head” and “tail” of a vector: a vector is, after all, a point in space; “direction”, “sense” and “magnitude” are uniquely identified by giving the coordinates of such a point (which would be the “head” of the vector), because “direction” is the line uniquely identified by the point in space and the origin, “sense” is also unequivocal because it’s always away from the origin (which is the reason why in maths nobody cares about the sense of a vector) and magnitude has the more precise name of norm.
Answer:
[1/3✓/1/3✓\1/3] these is the correct answer