Locus of the point P, for which `vec(OP)` represents a vector with direction cosine `cos alpha = (1)/(2)` (where O is the origin) is

The direction cosines of the line passing through P(2,3,-1) and the origin are

A variable line passing through point P(2,1) meets the axes at A and B . Find the locus of the circumcenter of triangle O A B (where O is the origin).

A variable line through the point P(2,1) meets the axes at A an d B . Find the locus of the centroid of triangle O A B (where O is the origin).

Lelt two non collinear unit vectors hata and hatb form and acute angle. A point P moves so that at any time t the position vector vec(OP) (where O is the origin) is given by hatacost+hatbsint. When P is farthest from origin O, let M be the length of vec(OP) and hatu be the unit vector along vec(OP) Then (A) hatu= (hata+hatb)/(|hata+hatb|) and M=(1+hata.hatb)^(1/2) (B) hatu= (hata-hatb)/(|hata-hatb|) and M=(1+hata.hatb)^(1/2) (C) hatu= (hata+hatb)/(|hata+hatb|) and M=(1+2hata.hatb)^(1/2) (D) hatu= (hata-hatb)/(|hata-hatb|) and M=(1+2hata.hatb)^(1/2)

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to (1, -2, -2) and (0, 2, 1)

Let two non-collinear vectors veca and vecb inclined at an angle (2pi)/(3) be such that |veca|=3 and vec|b|=2 . If a point P moves so that at any time t its position vector vec(OP) (where O is the origin) is given as vec(OP) = (t+1/t)veca+(t-1/t)vecb then least distance of P from the origin is

Let PN be the perpendicular from the point P(1, 2, 3) to xy-plane. If OP makes an angle alpha with positive direction of the z-axis and ON makes an angle beta with the positive direction of x-axis, where O is the origin ( alpha and beta are acute angles), then

Write the direction cosines of the vector vec r=6 hat i-2 hat j+3 hat kdot

Find the direction cosines of the line which is perpendicular to the lines with direction cosines proportional to 1, -2, -2 and 0, 2, 1

If P be the point (2,6, 3) then the equation of the plane through P, at right angles to OP, where 'O' is the origin is