The position vectors of `Pa n dQ` are 5` hat i+4 hat j+a hat k` and `- hat i+2 hat j-2 hat k` , respectively. If the distance between them is 7, then find the value of `adot`

The position vector of the points Pa n dQ are 5 hat i+7 hat j-2 hat k and -3 hat i+3 hat j+6 hat k , respectively. Vector vec A=3 hat i- hat j+ hat k passes through point P and vector vec B=-3 hat i+2 hat j+4 hat k passes through point Q . A third vector 2 hat i+7 hat j-5 hat k intersects vectors Aa n dBdot Find the position vectors of points of intersection.

Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k , respectively. Vector hat i- hat j+6 hat k is perpendicular to the plane containing the origin and the points Pa n dQ . Then lambda equals 1//2 b. 1//2 c. 1 d. none of these

Let the position vectors of the points Pa n dQ be 4 hat i+ hat j+lambda hat ka n d2 hat i- hat j+lambda hat k , respectively. Vector hat i- hat j+6 hat k is perpendicular to the plane containing the origin and the points Pa n dQ . Then lambda equals 1//2 b. 1//2 c. 1 d. none of these

Find the equation of the sphere described on the joint of points Aa n dB having position vectors 2 hat i+6 hat j-7 hat ka n d-2 hat i+4 hat j-3 hat k , respectively, as the diameter. Find the center and the radius of the sphere.

Find the angle between the vectors hat i - 2 hat j + 3 hat k and 3 hat i - 2 hat j + hat k .

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are hat i + 2 hat j - hat k and - hat i + hat j + hat k respectively, in the ratio 2 : 1 (i) internally (ii) externally

Find the position vector of a point R which divides the line joining two points P and Q whose position vectors are hat i + 2 hat j - hat k and - hat i + hat j + hat k respectively, in the ratio 2 : 1 (i) internally (ii) externally

The position vectors of the points Pa n dQ with respect to the origin O are vec a= hat i+3 hat j-2 hat k and vec b=3 hat i- hat j-2 hat k , respectively. If M is a point on P Q , such that O M is the bisector of angleP O Q , then vec O M is a. 2( hat i- hat j+ hat k) b. 2 hat i+ hat j-2 hat k c. 2(- hat i+ hat j- hat k) d. 2( hat i+ hat j+ hat k)

The position vectors of the point A ,B ,Ca n dDa r e3 hat i-2 hat j- hat k ,2 hat i+3 hat j-4 hat k ,- hat i+ hat j+2 hat k and 4 hat i+5 hat j+lambda hat k , respectively. If the points A ,B ,Ca n dD lie on a plane, find the value of lambdadot

If the vectors 3 hat i + lambda hat j + hat k and 2 hat i - hat j + 8 hat k are perpendicular, then lambda is