Find the parametric form of vector equation of a line passing through a point `(2,-1,3)` and parallel to line `vec(r)=(hat(i)+hat(j))+t(2hat(i)+hat(j)-2hat(k))`

Find the parametric form of vector eqution of the straight line passing through (-1,2,1) and paralle to the straight line vec(r)=(2hat(i)+3hat(j)-hat(k))+t(hat(i)-2hat(j)+hat(k)) and lines find the shortest distance between the lines.

Find the parametric form of vector equation, and Cartesian equations of the plane containing the line vec(r)=(hat(i)-hat(j)+3hat(k))+t(2hat(i)-hat(j)+4hat(k))" and perpendicular to plane "vec(r)*(hat(i)+2hat(j)+hat(k))=8.

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.

Find the non-parametric form of vector equation, and Cartesian equations of the plane vec(r)=(6hat(i)-hat(j)+hat(k))+s(-hat(i)+2hat(j)+hatk)+t(-5hat(j)-4hat(j)-5hat(k))

Find the non-parametric form of vector equation and Cartesian equations of the straight line passing through the point with position vector 4hat(i)+3hat(j)-7hat(k)" and parallel to the vector "2hat(i)-6hat(j)+7hat(k).

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

Find the point where line which passes through point (1,2,3) and is parallel to line vec r= hat i+ hat j+2 hat k+lambda( hat i-2 hat j+3 hat k) meets the xy-plane.

Line L_1 is parallel to vector vecalpha=-3 hat i+2 hat j+4 hat k and passes through a point A(7,6,2) and line L_2 is parallel vector vecbeta=2 hat i+ hat j+3 hat k and point B(5,3,4)dot Now a line L_3 parallel to a vector vec r=2 hat i-2 hat j- hat k intersects the lines L_1a n dL_2 at points Ca n dD , respectively, then find | vec C D|dot

Find a vector whose length is 7 and that is perpendicular to each of the vectors vec(A) = 2 hat(i) - 3 hat(j) + 6 hat(k) and vec(B) = hat(i) + hat(j) - hat(k)