Home
Class 12
MATHS
A line O P through origin O is inclined ...

A line `O P` through origin `O` is inclined at `30^0a n d45^0toO Xa n dO Y ,` respectivley. Then find the angle at which it is inclined to `O Zdot`

Text Solution

Verified by Experts

Let `l, m and n` be the direction coisines of the given vector. Then `l^(2)+m^(2)+n^(2)=1`.
If `l=cos30^(@)=sqrt(3)//2, m=cos45^(@)=1//sqrt(2),"then "(3)/(4)+(1)/(2)+n^(2)=1`.
`rArr" "n^(2)=-1//4`, which is not possible. So, such a line cannot exist.
Promotional Banner

Topper's Solved these Questions

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.1|12 Videos

  • THREE-DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise CONCEPT APPLICATION EXERCISE 3.2|15 Videos

  • THREE DIMENSIONAL GEOMETRY

    CENGAGE PUBLICATION|Exercise All Questions|291 Videos

  • TRIGONOMETRIC EQUATIONS

    CENGAGE PUBLICATION|Exercise Archives (Numerical value type)|4 Videos

Similar Questions

Explore conceptually related problems

A straight line is drawn through P(3,4) to meet the axis of x and y at Aa n dB , respectively. If the rectangle O A C B is completed, then find the locus of Cdot

A straight line through the origin 'O' meets the parallel lines 4x +2y= 9 and 2x +y=-6 at points P and Q respectively. Then the point 'O' divides the segment PQ in the ratio : (A) 1:2 (B) 3:2 (C) 2:1 D) 4:3

The line x+y=p meets the x- and y-axes at Aa n dB , respectively. A triangle A P Q is inscribed in triangle O A B ,O being the origin, with right angle at QdotP and Q lie, respectively, on O Ba n dA B . If the area of triangle A P Q is 3/8t h of the are of triangle O A B , the (A Q)/(B Q) is equal to (a) 2 (b) 2/3 (c) 1/3 (d) 3

A straight line is drawn through the point P(2,3) and is inclined at an angle of 30^@ with the x-axis . Find the coordinates of two points on it at a distance 4 from point P.

Two men Pa n dQ start with velocity u at the same time from the junction of two roads inclined at 45^0 to each other. If they travel by different roads, find the rate at which they are being separated.

If arcs of same length in two circles subtend angles of 30^0a n d45^0 at their centers, find the ratios of their radii.

A line passing through the origin O(0,0) intersects two concentric circles of radii aa n db at Pa n d Q , If the lines parallel to the X-and Y-axes through Qa n dP , respectively, meet at point R , then find the locus of Rdot

A line passing through the point P(4,2) meets the x and y-axis at A and B respectively. If O is the origin, then locus of the centre of the circumcircle of triangle OAB is

The coordinates of O , A and B are (0,0) , (x,y) and (y,x) respectively. If angle AOB=theta, then the value of cos theta is-

Find the equations of the lines which pass through the origin and are inclined at an angle tan^(-1)m to the line y=m x+c dot