If i, j and k are unit vectors along x-axis, y axis and z axis then i.j = j.k = i.k =
A. 0
B. 1/2
C. 1
D. none of these
A. 0
In the case of unit vectors i, j, and k representing the x, y, and z axes respectively, then i.j = j.k = i.k = 0.
Here’s why:
- The dot product (represented by .) of two vectors calculates the magnitude of their projection onto each other.
- Since i, j, and k are orthogonal (perpendicular) unit vectors, their projections onto each other will be zero.
- Imagine a vector along the x-axis (i) and another along the y-axis (j). Projecting i onto j would result in a zero vector because i has no component in the y-direction. Similarly, projecting j onto i or any other two unit vectors will result in zero.
Therefore, the dot product of any two of these unit vectors will be 0.
If i, j and k are unit vectors along x-axis, y axis and z axis then i.j = j.k = i.k = Read More »