Find the vector equation of the line passing through the point (1,2,3) and parallel to the vector `3hat(i) + lamda hat(j) - 2hat(k)`.

Find the vector equation of the line passing through the point (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)=5 and vec rdot(3 hat i+ hat j+ hat k)=6.

Find the vector equation of a line through the point (5, 2, -4) and which is parallel to the vector 3 hat(i) + 2 hat(j) - 8hatk ?

Find the vector equation for the line which passes through the point (1, ,2 3) and parallel to the vector hat i-2 hat j+3 hat kdot reduce the corresponding equation in the Cartesian from.

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 3 hat i+2 hat j-2 hat k .

Find the equation of the line which passes through the point (1, 2, 3) and is parallel to the vector 6 hat i+4 hat j-2 hat k .

Write the vector equation of the line passing through the point (1, -2, -3) and normal to the plane vec rdot((2 hat i+ hat j+2 hat k)=5.

Find the vector equation of the line passing through (2,1,-1) and parallel to the line vec r= (hat i+hat j)+lambda(2hat i-hat j+hat k) . Also, find the distance between these two lines.

Find the equation of a line passing through a point (2, -1, 3) and parallel to the line vec r=( hat i+ hat j)+lambda(2 hat i+ hat j-2 hat k)dot

Find the vector and cartesian equations of the line passing through the point P\ (1,\ 2,\ 3)\ and parallel to the planes vec rdot( hat i-\ hat j+2 hat k)=5\ and vec rdot(3 hat i+ hat j+ hat k)=6.

Find the vector equation of the line passing through (1,2,3) and parallel to the planes vec rdot( hat i- hat j+2 hat k)a n d vec rdot(3 hat i+ hat j+ hat k)=6.