Find the position vector of the mid-point of the vector joining the points `P(2 hat i-3 hat j+4 hat k"")a n d"Q"(4 hat i+ hat j-2 hat k)dot`

Find the position vector of the mid-point of the vector joining the points P(2hat i-3hat j+4hat k) and Q(4hat i+hat j-2hat k)

Write the position vector of a point dividing the line segment joining points having position vectors hat i+ hat j-2 hat k\ a n d\ 2 hat i- hat j+3 hat k externally in the ratio 2:3.

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

Find the vector equation of the plane passing through three points with position vectors hat i+ hat j-2hatk, 2hat i-\ hat j+ hat k and hat i+2 hat j+ hat kdot Also find the coordinates of the point of intersection of this plane and the line vec r=3 hat i-\ hat j- hat k+lambda(2 hat i-\ 2 hat j+ hat k)dot

Find the vector equation of the plane passing through three points with position vectors hat i+ hat j-2hatk, 2hat i-\ hat j+ hat k and hat i+2 hat j+ hat kdot Also find the coordinates of the point of intersection of this plane and the line vec r=3 hat i-\ hat j- hat k+lambda(2 hat i-\ 2 hat j+ hat k)dot

Find the vector equation of a line passing through a point with position vector 2hat i-hat j+hat k ,and parallel to the line joining the points -hat i+4hat j+hat k and hat i+2hat j+2hat k. Also, find the cartesian equivalent of this equation.

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

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