Q. 44.3( 30 Votes )

If a line makes angles 90°, 135°, 45° with x, y and z axes respectively, find its direction cosines.
Or
Find the vector equation of the line which passes through the point (3,4,5) and is parallel to the vector .

Answer :

Direction cosines of a line making angle α with x-axis, β with y-axis and γ with z-axis are l, m ,n.

l = cos α , m = cos β , n = cos γ

Here, α = 90° , β = 135° and γ = 45°

l = cos 90°

=0

m = cos 135°

= cos(180° - 45°)

= -cos 45°

n = cos 45°


OR


If the coordinates of a point A= (x1, y1, z1), then the position vector is



Hence, the position vector of point P = (3,4,5) is


If the position vector () of a point on the line and a vector () parallel to the line is given, then the vector equation of a line is given by



Here, and , then



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