Write down the vector equation of the line that passes through the points (x,y,z) = (2,3,7) and (x,y,z)= (4,1,2)

Draw the vectors in standard position in R2 with their tails at the point (2, -3).

Consider (13,3,7) in vector space. Find symmetric equations of a line that contains the point (13,3,7) and the origin. Demonstrate how to check (13,3,7) and (0,0,0) that they fit the equation of the line.

16. Determine the vector equation of each line. a) parallel to the y-axis and through Po(-4, 11) b) perpendicular to 5x - 2y = 3 and through Po(7, 1) c) parallel to x + 6y = 1 and through Po(2,-5) d) parallel to the z-axis and through Po(-4, 3, 7) e) parallel to [x, y, z]= [1, 3, -2] + [5, 2, 1] f) the x-intercept of the line is 3 and the y-intercept is -2

Write the vector equation of the line through (9,-1) and perpendicular to (x,y) = (1,-2) + t(6,-7)

4(2). Please show your calculations & explain steps by steps. Determines the vector equation: A) from the line in R2 that goes through the points (3, -6) and (0, -1). B) of the plan in R3 that contains the points (-6, 1, 0), (4, -3, 5) ret (-7, -2, -4).

Determine the vector equation for the line that is parallel to 7 = [1,5,-7]+t[2,-1,5] with the same x-intercept as [x, y, z]=[-1,8,6]+t[-2,4,3]. 3.