Parametric equations a line are x=2-3t, y=-1+2t and z=3+t. write down the vector equations of the line.

Parametric equations of a line are x=-1+2t, y=3-4t and z=2+t. find the equations of the line in the symmetrical form.

If the cartesian equations of a line are : (3-x)/5=(y+4)/7=(2z-6)/4 , write the vector equation for the line.

The Cartesian equation of a line is (x-3)/2=(y+1)/(-2)=(z-3)/5 . Find the vector equation of the line.

The Cartesian equation of a line is (x+3)/2 = (y-5)/4 = (z+6)/2 . Find the vector equation for the line.

The cartesian equation of a line are 6x-2=3y+1=2z-2 . Find its direction ratios and also find the vector of the line.

The cartesian equation of a line is 6x - 2 = 3y + 1 = 2z - 2 . Find :(a) the direction-ratios of the line, and (b) vector equation of the line parallel to this line and· passing through the point (2, - 1, - 1).

Find x and y if the point (x,-1,3), (3,y,1) and (-1,11,9) are collinear. Also, write down the vector equation of the line in which they lie. Further, find the point of intersection of this line and the plane x+y+z+1=0 .

The cartesian equations of a line are : (x-5)/3=(y+4)/7=(z-6)/2 and (x+3)/2=(y-5)/4=(z+6)/2 . find the vector equation of the lines.

Computing area with parametrically represented boundaries If the boundary of a figure is represented by parametric equations x = x (t) , y = y(t) , then the area of the figure is evaluated by one of the three formulae S = -underset(alpha)overset(beta)(int) y(t) x'(t) dt , S = underset(alpha) overset(beta) (int) x (t) y' (t) dt S = (1)/(2) underset(alpha)overset(beta)(int) (xy'-yx') dt where alpha and beta are the values of the parameter t corresponding respectively to the beginning and the end of traversal of the contour . The area enclosed by the astroid ((x)/(a))^((2)/(3)) + ((y)/(a))^((2)/(3)) = 1 is

Find the vector equation of the line (x+4)/3=(y+3)/7=(z-5)/2