Q. 115.0( 5 Votes )

# The projections of a line segment on X, Y and Z axes are 12, 4 and 3 respectively. The length and direction cosines of the line segment are

A.

B.

C.

D. none of these

Answer :

If a line makes angles α , β and γ with the axes then,

cos^{2}α + cos^{2}β + cos^{2}γ = 1 → (1)

Let ‘r’ be the length of the line segment.

Then,

rcosα = 12, rcosβ = 4, rcosγ = 3 → (2)

Now,

(rcosα)^{2} + (rcosβ)^{2} + (rcosγ)^{2} = 12^{2} + 4^{2} + 3^{2} → From (2)

r^{2} (cos^{2}α + cos^{2}β + cos^{2}γ) = 169

r^{2} (1) = 169 → From (1)

r

r

r = 13 → (Since length cannot be negative)

Substituting r = 13 in (2) , we get

cosα , cosβ , cosγ

Thus, the direction cosines of the line are - , , .

Rate this question :

Write the direction cosines of a line equally inclined to the three coordinate axes.

Mathematics - Board PapersFind the angle between the following pair of lines:

and

and check whether the lines are parallel or perpendicular.

Mathematics - Board PapersFind the coordinates of the foot of perpendicular, and the perpendicular distance from the point P(4, 3, 2) to the plane Also find the image of P in the plane.

Mathematics - Board PapersFind a vector of magnitude 5√2, making an angle of with x-axis., with y-axis and an acute angle θ with z-axis.

Mathematics - Board PapersIf a line makes angles 90°, 60° and θ with x, y and z-axis respectively, where θ is acute, then find θ.

Mathematics - Board Papers