Find the vector equation of a line which is parallel to the vector `2 hat i- hat j+3 hat k` and which passes through the point (5, -2,4). Also reduce it to Cartesian form.

Find the equation of straight line parallel to 2hat(i)-hat(j)+3hat(k) and passing through the point (5, -2, 4) .

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 a vector of magnitude 9, which is perpendicular to both vectors 4 hat i- hat j+3 hat ka n d-2 hat i+ hat j-2 hat k .

Find the vector equation of a line which passes through the point with position vector 2 hat i= hat j+4 hat k and is in the direction of hat i+ hat j-2 hat kdot Also, reduce it to Cartesian form.

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 .

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

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to the plane 3x-4y+5z=8.

Find the vector equation of a line passing through 3 hat i-5 hat j+7 hat k and perpendicular to theplane 3x-4y+5z=8.

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.