Q.Find the vector and Cartesian equations of the line passing through the points $A(2,-1,3)$ and $B(5,2,7)$.

Direction ratios of $AB$: $x_2-x_1,\,y_2-y_1,\,z_2-z_1 = 5-2,\ 2-(-1),\ 7-3 = 3,3,4$.

Vector equation (base point $A$):

Cartesian equation: …

Compute the direction ratios as the coordinate differences between the two given points, then substitute the direction ratios and e …

Writing $(y+1)$ as $(y-1)$ by mishandling the double negative from $y_1=-1$; using $B$ as the base point but $A$'s coordin …