Determine the vector equation of a plane that contains the line with symmetric x+3 equation *+-+12+2 and the point P(1,3,0). 5 7- (1,3,0) + s(-2,5,4) + t(3, 1, 2), s,t € R OF(1,3,0) + s(-2,5,4) + (4,4,2), s,£ € R OF(1,3,0) + 5 (-2,5,4) + (1,3,0), s,£ € R none of the above

Suppose vector a= (4, -6, 10) and vector B= (-6, 9, -15). What is a x b?

Please give me answer very fast in 5 min

Find the equation for the plane through the point Po = (2,10,7) and normal to the vector n= 9i + 2j + 2k. Using a coefficient of 9 for x, the equation for the plane through the point Po = (2,10,7) and normal to n= 9i + 2j + 2k is |.

Let L, be the line passing through the points Q₁-(-1,-3, 1) and Q2-(-4, -6, 2). Find a value of k so the line L2 passing through the point P₁-P₁(-14, 12, k) with direction vector -[-2, 6, -5] intersects with L₁- k = 0

b) Adam walks in a straight line form the point A(-1, 4) to the point Q(4, 16) with constant speed. His position vector can be expressed in the form p = a + tu, where t is the time after he starts walking. Adam arrives at the point Q at t = 3. ~ A (-1,4) i. State the vectors a and u. y Q(4,16) B (11,9) ii. Bob is at point B(11,9). During Adam's walk from A to P, Bob wishes to throw a ball to Adam. Bob decides to throw the ball when Adam is at the closest point to B. a) Write a vector w that is perpendicular to u. B) Hence or otherwise, find value of t when Bob throws the ball to Adam.

Suppose that a plane contains the points (5, 0, 0) and (0, 3, 1) and the line with the vector equation r = t < 2.5, 1.5, 0.5 >. What is the equation of the line?   Please explain your steps and show work.

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.