Q20 of 177 Page 24

Write the length (magnitude) of a vector whose projections on the coordinate axes are 12, 3 and 4 units.

Since L_x=12, L_y=3 and L_z=4 are given, we can find out L by

L²= L_x²+L_y²+L_z²

=12²+3²+4²

=144+9+16=169

Hence L=13 units.

If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin²α + sin²β + sin²γ.

Write a vector of magnitude 12 units which makes 45° angle with X-axis, 60° angle with y-axis and an obtuse angle with Z-axis.

Write the position vector of a point dividing the line segment joining points A and B with position vectors externally in the ratio 1 : 4, where and

Write the direction cosines of the vector