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`

A line is inclined to the x-axis at 45^@ and y-axis at 60^@ . Find the angle at which the line is inclined to z-axis.

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

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

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.

Two circles C_1a n dC_2 intersect at two distinct points Pa n dQ in a line passing through P meets circles C_1a n dC_2 at Aa n dB , respectively. Let Y be the midpoint of A B ,a n dQ Y meets circles C_1a n dC_2 at Xa n dZ , respectively. Then prove that Y is the midpoint of X Zdot

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

O A and O B are fixed straight lines, P is any point and P M and P N are the perpendiculars from P on O Aa n dO B , respectively. Find the locus of P if the quadrilateral O M P N is of constant area.

Let P and Q be any two points on the lines represented by 2x-3y = 0 and 2x + 3y = 0 respectively. If the area of triangle OPQ (where O is origin) is 5, then which of the following is not the possible equation of the locus of mid-point of PO? (a) 4x^2-9y^2 +30 = 0 (b) 4x^2-9y^2-30 = 0 (c) 9x^2-4y^2-30=0 (d) none of these

If O is the origin, O P=3 with direction ratios -1,2,a n d-2, then find the coordinates of Pdot