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.

A line passes through the point with position vector 2 hat i-3 hat j+4 hat k and is in the direction of 3 hat i+4 hat j-5 hat kdot Find equations of the line in vector and Cartesian form.

Find the equation of the line in vector and in cartesian form that passes through the point with position vector 2hat i-hat j+4hat k and is in the direction hat i+2hat j-hat k

Find the vector equation of a plane passing through a point having position vector 2 hat i- hat j+ hat k and perpendicular to the vector 4 hat i+2 hat j-3 hat kdot

A line passes through the point with position vector 2hat i-3hat j+4k is in the direction of 3hat i+4hat j-5hat k. Find the equations of the line in vector and Cartesian forms.

Find the Cartesian equation of a line which passes through the point having position vector (2hat(i) -hat(j) + 4hat(k)) and is in the direction of the vector , (hat(i) +2hat(j) -hat(k))

A line passes through the point with position vector 2hat(i)-3hat(j)+4hat(k) and is in the diretion of 3hat(i)+4hat(j)-5hat(k) . Find the equation of the line is vector and cartesian forms.

Find the vector equation of a plane passing through the point having position vector 2 hat(i) + hat(j) + hat(k) and perpendicular to the vector : 4 hat(i) - 2 hat(j) + 3hat(k) .

Find the vector equations of the line passing through the point with position vector (2hat(i) +hat(j) -5hat(k)) and parallel to the vector (hat(i) +3hat(j) -hat(k)) .Deduce the Cartesian equations of the line .

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

Find the vector equation of the line which passes through the point (3,4,5) and is parallel the vector 2 hat(i) + 2 hat(j) - 3 hat(k) .