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 vectors of P and Q are 5hat i+4hat j+ahat k and -hat i+2hat j-2hat k, respectively. If the distance between them is 7, then find the value of a.

Find the projection (vector) of the vector 7 hat i+ hat j- 4 hat k on 7 hat i+ hat j- 3 hat k .

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.

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 A,B,C be points with position vectors 2hat i-hat j+hat k,hat hat i+2hat j+hat k and 2hat i+hat j+2hat k respectively.Find the shortest distance between point B and plane OAC.

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 a -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

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

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 a -1//2 b. 1//2 c. 1 d. none of these