English

What Are the Direction Cosines of Y-axis?

Advertisements
Advertisements

Question

What are the direction cosines of Y-axis?

Sum
Advertisements

Solution

\[ \text{ The y - axis makes angles 90°, 0° and 90° with x, y and z axes, respectively } . \]

\[\text{ Therefore, the direction cosines of y - axis are cos 90°, cos 0°, cos 90° , i . e  }. 0, 1, 0 .\]

 

shaalaa.com
  Is there an error in this question or solution?
Chapter 26: Direction Cosines and Direction Ratios - Very Short Answers [Page 24]

APPEARS IN

RD Sharma Mathematics Volume 1 and 2 [English] Class 12
Chapter 26 Direction Cosines and Direction Ratios
Very Short Answers | Q 3 | Page 24

RELATED QUESTIONS

Write the direction ratios of the following line :

`x = −3, (y−4)/3 =( 2 −z)/1`


If a line makes angles 90°, 135°, 45° with the X, Y, and Z axes respectively, then its direction cosines are _______.

(A) `0,1/sqrt2,-1/sqrt2`

(B) `0,-1/sqrt2,-1/sqrt2`

(C) `1,1/sqrt2,1/sqrt2`

(D) `0,-1/sqrt2,1/sqrt2`


Find the angle between the lines whose direction ratios are 4, –3, 5 and 3, 4, 5.


If a line has the direction ratios −18, 12, −4, then what are its direction cosines?


Find the Direction Cosines of the Sides of the triangle Whose Vertices Are (3, 5, -4), (-1, 1, 2) and (-5, -5, -2).


If l1m1n1 and l2m2n2 are the direction cosines of two mutually perpendicular lines, show that the direction cosines of the line perpendicular to both of these are m1n2 − m2n1n1l2 − n2l1l1m2 ­− l2m1.


If a line makes angles of 90°, 60° and 30° with the positive direction of xy, and z-axis respectively, find its direction cosines


Find the angle between the vectors with direction ratios proportional to 1, −2, 1 and 4, 3, 2.


Find the angle between the vectors whose direction cosines are proportional to 2, 3, −6 and 3, −4, 5.


Find the angle between the lines whose direction ratios are proportional to abc and b − cc − aa− b.


Find the direction cosines of the lines, connected by the relations: l + m +n = 0 and 2lm + 2ln − mn= 0.


Find the angle between the lines whose direction cosines are given by the equations

2l + 2m − n = 0, mn + ln + lm = 0


Define direction cosines of a directed line.


Write the distances of the point (7, −2, 3) from XYYZ and XZ-planes.


Write the distance of the point (3, −5, 12) from X-axis?


If a line makes angles α, β and γ with the coordinate axes, find the value of cos2α + cos2β + cos2γ.


Write the angle between the lines whose direction ratios are proportional to 1, −2, 1 and 4, 3, 2.


Write the coordinates of the projection of the point P (2, −3, 5) on Y-axis.


If a unit vector  `vec a` makes an angle \[\frac{\pi}{3} \text{ with } \hat{i} , \frac{\pi}{4} \text{ with }  \hat{j}\] and an acute angle θ with \[\hat{ k} \] ,then find the value of θ.


A rectangular parallelopiped is formed by planes drawn through the points (5, 7, 9) and (2, 3, 7) parallel to the coordinate planes. The length of an edge of this rectangular parallelopiped is


Find the direction cosines of the line joining the points P(4,3,-5) and Q(-2,1,-8) . 


Verify whether the following ratios are direction cosines of some vector or not

`1/sqrt(2), 1/2, 1/2`


Find the direction cosines of a vector whose direction ratios are

`1/sqrt(2), 1/2, 1/2`


Find the direction cosines and direction ratios for the following vector

`3hat"i" - 4hat"j" + 8hat"k"`


Find the direction cosines and direction ratios for the following vector

`hat"j"`


Find the direction cosines and direction ratios for the following vector

`hat"i" - hat"k"`


If (a, a + b, a + b + c) is one set of direction ratios of the line joining (1, 0, 0) and (0, 1, 0), then find a set of values of a, b, c


Find the direction cosines of the line passing through the points P(2, 3, 5) and Q(–1, 2, 4).


If α, β, γ are the angles that a line makes with the positive direction of x, y, z axis, respectively, then the direction cosines of the line are ______.


A line makes equal angles with co-ordinate axis. Direction cosines of this line are ______.


If the directions cosines of a line are k,k,k, then ______.


The d.c's of a line whose direction ratios are 2, 3, –6, are ______.


Find the coordinates of the foot of the perpendicular drawn from point (5, 7, 3) to the line `(x - 15)/3 = (y - 29)/8 = (z - 5)/-5`.


Find the coordinates of the image of the point (1, 6, 3) with respect to the line `vecr = (hatj + 2hatk) + λ(hati + 2hatj + 3hatk)`; where 'λ' is a scalar. Also, find the distance of the image from the y – axis.


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×