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Relation between the direction cosines of a line, Direction cosines of a line passing through two points
- 3 Dimensional Geometry part 4 (Example:- Direction cosine, ratio)
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- 3 Dimensional Geometry part 3 (Example:- Direction cosine, ratio)
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- 3 Dimensional Geometry part 2 (Direction Cosine, Ratios)
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- 3D Geometry Straight Line Part 01 (Direction ratio, Direction Cosines)
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- Three Dimensional Geometry Part 1- Direction Ratios
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If l, m, n are the direction cosines of a line, then prove that l2 + m2 + n2 = 1. Hence find the
direction angle of the line with the X axis which makes direction angles of 135° and 45° with Y and Z axes respectively.
If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.
If a line makes angles 90°, 135°, 45° with x, y and z-axes respectively, find its direction cosines.
If l1, m1, n1 and l2, m2, n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1, n1l2 − n2l1, l1m2 − l2m1.
If the lines `(x-1)/(-3) = (y -2)/(2k) = (z-3)/2 and (x-1)/(3k) = (y-1)/1 = (z -6)/(-5)` are perpendicular, find the value of k.
Find the vector equation of the plane passing through (1, 2, 3) and perpendicular to the plane `vecr.(hati + 2hatj -5hatk) + 9 = 0`
Direction cosines of the line passing through the points A (- 4, 2, 3) and B (1, 3, -2) are.........
Find the direction cosines of the line perpendicular to the lines whose direction ratios are -2, 1,-1 and -3, - 4, 1