If a→=i+j-2k then the direction cosines are______.
The direction cosines of a vector are the cosines of the angles that the vector makes with the positive x, y, and z axes.
In this case, the vector a is given by a = i + j - 2k.
To find the direction cosines, we need to normalize the vector a by dividing it by its magnitude. The magnitude of a vector is given by the square root of the sum of the squares of its components.
Magnitude of a = √(1^2 + 1^2 + (-2)^2) = √(1 + 1 + 4) = √6
So, the normalized vector A is given by A = (1/√6)i + (1/√6)j + (-2/√6)k.
The direction cosines of the vector a are the coefficients of i, j, and k in the normalized vector A.
Therefore, the direction cosines of a are:
cosine of the angle with the x-axis = (1/√6)
cosine of the angle with the y-axis = (1/√6)
cosine of the angle with the z-axis = (-2/√6)