A millionaire bought a lot of hats `1/4` of which were brown. The millionaire sold `2/3` of the hats including `4/5` of the brown hats. What fraction of the unsold hats were brown? `1/(60)` (b) `1/(15)` (c) `3/(20)` (d) `3/5` (e) `3/4`

Find a vector whose length is 3 and which is perpendicular to the vector vec a=3hat i+hat j-4hat k and vec b=6hat i+5hat j-2hat k

The vector hat i+xhat j+3hat k is rotated through an angle theta and doubled in magnitude,then it becomes 4hat i+(4x-2)*hat j+2hat k. Then value of x are -(2)/(3)(b)(1)/(3)(c)(2)/(3)(d)2

If the resultant of the vectors 3hat i+4hat j+5hat k and 5hat i+3hat j+4hat j makes an angle thetawithx -axis, then find cos theta

Show that the points whose position vectors are 5hat i+5hat k,2hat i+hat j+3hat k and -4hat i+3hat j-hat k are collinear

The angle between the two vectors vec A= 3 hat i + 4 hat j + 5 hat k and vec B = 3 hat i + 4 hat j + 5 hat k will be

Find the moment about (1,-1,-1) of the force 3hat(i)+4hat(j)-5hat(k) acting at (1, 0,-2) .

Show that the points A(-2 hat i+3 hat j+5 hat k), B( hat i+2 hat j+3 hat k) and C(7 hat i-3 hat k) are collinear.

The position vectors of points A, B, C are respectively hat i- hat j-3 hat k ,2 hat i+ hat j-2 hat k and -5 hat i+2 hat j-6 hat k . If the internal angular bisector of /_A in A B C meet BC at D, then length of AD is 1/4 (2) (11)/2 (3) (15)/2 (4) (3sqrt(10))/4

Let the centre of the parallelepiped formed by vec P A= hat i+2 hat j+2 hat k ; vec P B=4 hat i-3 hat j+ hat k ; vec P C=3 hat i+5 hat j- hat k is given by the position vector (7, 6, 2). Then the position vector of the point P is (3,4,1) (b) (6,8,2) (1, 3, 4) (d) (2, 6, 8)

Area of a rectangle having vertices A, B, C and D with position vectors - hat i+1/2 hat j+4 hat k , hat i+1/2 hat j+4 hat k , hat i-1/2 hat j+4 hat k and - hat i-1/2 hat j+4 hat k respectively is (A) 1/2 (B) 1 (C) 2 (D) 4