Suppose P : : ax+by+cz = d Q: a'x+by+c' z = d' are two planes in 3-space. Which of the following statements are correct? (Select all that apply.) 000 If P and Q are perpendicular then the vectors (a,b,c) and (a',b,c') are perpendicular. If P and Q coincide (are the same plane) then d=d'. If P and Q are parallel then the vector (a,b,c) is a scalar multiple of (a',b',c'). If then P and Q are not parallel. a = a'

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

A:

Q: ex/IF Ā=i-j+3k and B =2 i+6j+3K Find the vector pricâ+B) and Prj (À-B).

A:

Q: In each part, find all the roots and sketch them as vectors in the complex plane. (a) (-i)//² (b)…

A: Note : Since you have posted a question with multiple subparts, we will provide the solution only to…

Q: One of the following vectors lies in span{ 2+x + x?, 3+x- 2x2} (A) 4+ x – 7r² (B) 4+ x – 4x? (C) 4 +…

A: Solve the following

Q: ) Find the vector that parallel to the intersection line of two planes 2x +y-3z 2 and -x+2y-z 1.

A: Given problem:- Find the vector that parallel to the intersection line of two planes 2x + y - 3z = 2…

Q: (1) Find the area of the triangle and indicate its type.

A:

Q: Q) Let û = 2745, Vz+3 , and w=T-5 find Scalars a and b such that u - av + bw

A:

Q: Three unique non-zero vectors a, b, and C are defined by four points in space. Select all of the…

A: Proceed as shown below

Q: 39. For each condition, find unit vectors å and b or explain why no such vectors exist. (a) |a+헤-0…

A:

Q: Let / be the line through the point with coordinates (1,-1,0) in the direction of the vector…

A:

Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

A:

Q: Let A be the point with coordinates (6, 3, 3) and let B be the point with coordinates (5, 3, 4). Let…

A:

Q: 4 r 1 by -1 -2 -3 -4 -5 -4 -3 -2 -10 1 2 3 4 5

A: First we find p, q, r and s. Then solve it.

Q: 27. Determine the area of the parallelogram formed by the vectors u=[3,-2,5] and v=[-1,4,2].

A: Step 1:

Q: 5. Let A = (4,3), B = (0, 1), and C = (−3, 7). (a) Find the vectors AB, BC, and AT. (b) Prove that…

A: Step 1:It is provided that, A=(4,3),B=(0,1), and C=(−3,7). (a) Then, it is obtained:AB=B−A…

Q: det pC-1,2,-1) and Q(2,-7,8) be two points in three dimenonal space. Use vectors to fird the points…

A: Vector form of a point: Let (a, b, c) are any point in 3D- space. Then this point can be expressed…

Q: Give v that is perpendicular to a plane containing (1,2,3), (3, 4, 1) and (-1, -2, -3). Check if…

A:

Q: 7. Let +-() वे = -2 and -4 2 3 Find a real number x and a vector such that = -x and 17.

A:

Q: 4. Express PQ-RO+SR-PS+RS as a single vector.

A:

Q: Please justify whether these statements are true of false. a. If u and v are vectors in R^3, then…

A: Objects with both magnitude and direction are called vectors. The vector's size is determined by the…

Q: Vectors a' and b are perpendicular to one another. Find k : a'(k², –k, 1), b´ (k, 3, – 2)

A: Scalar product of two vectors

Q: Find an equation of a plane containing the three points (0, -2, 4), (3, -3, 2), (3, -2, 4) in which…

A: The equation is  :-

Q: 9 find the cqu. f Plane that Contains the two line Ś: X-1=3+ 6=そ X=リニで-4 and Passes through origin?…

A:

Q: 16. For any vectors a, b and c, show that a. (axb) xc lies in the plane of a and b b. (a x b) X c =…

A: Step 1: Reference: Vector Calculus, Vector triple product

Q: a. A nonzero vector perpendicular to both [-1. 3, 4] and [-2. -1, 3].  b. The distance from (2, -1,…

A: Let's go through each of the questions:a. To find a nonzero vector perpendicular to both [−1,3,4]…

Q: 4 16 -- 12 -21 4. Is the vector in the span of the vectors 10 12 -8 and 8 ? Explain!

A: