Find the normal form of the equation of the plane that passes through
Find the vector form of the equation of the line in ℝ2 that passes through
P = (5, −2)
and is parallel to the line with general equation
5x − 4y = 2.
Find the normal form of the equation of the plane that passes through Find the vector...
(a). Find the equation of the plane through Po = (1,2,1) with normal vector i = (3,1,2) (b). Find the equation of a plane through Po = (2,3,1) and parallel to the plane P:3x + 2y -- z = 4 | Q4. Consider the line z-3 y-2 3 L, : * - - - L2: **** 2+5 y-3 -1 2 (i). Write the equations of both lines in parametric form (ii). Find the direction vectors V1, V2 of the lines...
Find the general equation and a vector equation of the plane that passes through the points p(1,2,4) Q(1,-1,6) R(1,4,8)
Find an equation of the plane that passes through the point P(-2, -3,4) and has the vector n = (-8,7,2) as a normal. Edit III
Use the cross product to help find the normal form of the equation of a plane. 4. Use the cross product to help find the normal form of the equation of the plane. a. The plane passing through P= (1,0, –2), parallel to [0] u= 1 and v= -1 [ 2] b. The plane passing through P= (0,-1,1), Q = (2,0, 2), and R= (1, 2, -1)
09: Find the equation of the plane that passes through (1,1,1) and has (-1,2,4) as normal. Q10: Decide whether the planes are parallel, orthogonal or neither: 2x+y=3 3x-y+4z=10
I 7. Find the equation of the line in the slope-intercept form that passes through (-3,2) and is parallel to the line 2x + 3y = 6. Graph and label both lines in the same coordinate plane. 41
Find parametric equations of the plane that passes through the origin and has normal vector (3, 1, −6).
10. Express the following in vector form: a. Line IcR that passes through the points A-(-1,-1,0) and B = (2, 3, 5) b. Plane P Rwhich passes through the appoints A = (1, 1,-1,-1), B = (1,-1, 1,-1) and whose coordinates satisfy the equation x + y + 2z - W=3.
please answer question 16 and 17 17. Find the equation of a plane that passes through the points (15,5, 2), (6, 2, 1) and (10,3, 2). Does the point (-2,-5, -3) lie on the plane? [5 marks) 16. Find the equation of a line through the point (2, -3, 1) in a direction orthogonal to the line *+1 Y-1.2+2. Give your answer in both parametric and 3 5 symmetric form. [4 marks) 2
Q4. (5 points). Find the equation of the plane that passes through the line of intersection of the two planes x - 2y = 3 and y- z = 0 and parallel to the line x = y - 1 = 2+1 Q5. (4 points). Find the distance from the point A(1,2,3) and the line 2+1 y-1 2 Q6. (4 points). Give the name and sketch the surface whose equation is given by x2 + 2y2 – 12y – z...