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 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 equation of the plane passing through (3,4,-1), which is parallel to the plane vec rdot(2 hat i-3 hat j+5 hat k)+7=0.

Find the equation the plane which contain the line of intersection of the planes vec rdot( hat i+2 hat j+3 hat k)-4=0a n d vec rdot(2 hat i+ hat j- hat k)+5=0 and which is perpendicular to the plane vec r(5 hat i+3 hat j-6 hat k)+8=0 .

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

Find the unit vector perpendicular to the plane vec rdot(2 hat i+ hat j+2 hat k)=5.

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.

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 angle between the vectors ,When vec a = hat i -2 hat j +3 hat k and vec b = 3 hat i -2 hat j + hat k

Find a vector of magnitude 5 units, and parallel to the resultant of the vectors vec a = 2 hat i + 3 hat j - hat k and vec b = hat i - 2 hat j+ hat k

Find the vector equation of the following planes in Cartesian form: vec r= hat i- hat j+lambda( hat i+ hat j+ hat k)+mu( hat i-2 hat j+3 hat k)dot