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 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

Write the position vector of a point dividing the line segment joining points A and B with position vectors vec a\ a n d\ vec b externally in the ration 1:4 where vec a=2 hat i+3 hat j+4 hat k\ a n d\ vec b=- hat i+ hat j+ hat kdot

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

Find the vector equation of the plane passing through the points having position vectors hat i+ hat j-2 hat k ,2 i - hat j+ hat ka n d hat i+2 hat j+ hat kdot

Find the vector equation of a line passing through the point with position vector hat i-2 hat j-3 hat k and parallel to the line joining the points with position vectors hat i- hat j+4 hat ka n d2 hat i+ hat j+2 hat kdot Also, find the Cartesian equivalent of this equation.

Find the image of the point having position vector hat i+2 hat j+4 hat k in the plane vec r.(2 hat i- hat j+ hat k)+3=0.

Find the distance between the points A and B with position vectors hat i- hat j and 2 hat i+ hat j+2 hat kdot

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