Use vector method to find the area of the triangle with vertices A, B, C that shown in the figure below: A(3,1,4) B(-3,5,1) -> yk C(0,5,-4)

Q: Find the area of the parallelogram that has the given vectors u = i + j + k,      v = j + k as…

A: Given: Vectors are u→=i^+j^+k^ and v→=j^+k^. To Find: Area of the parallelogram and use a graphing…

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: Find the area of the triangle determined by the points P, Q, and R. Use * .the cross product of…

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Q: Find the distance from the point P(1, 4, 0) to the plane through A(0, 0, 0), B(2, 0, -1), and C(2,…

A: Given points A0,0,0 , B2,0,-1 & C2,-1,0The direction ratios of AB⇒2-0,0-0,-1-0=2,0,-1Similarly…

Q: Find the angle between the planes whose vector equations are 7-(2i + 2)- 36) =57-(3i -3) + Sk) = 3…

A: The solution to the the given question is explained below.

Q: Find the distance from the origin to the plane through the point (-6,3, -2) and having 5i - 3j° + 4k…

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Q: What is the area of the parallelogram formed by the two vectors = (1,5) and = (-3,-2)?

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Q: Find the cross products of vectors: u=(0,-4,2) and v=(-3,2,6). Find the area of the parallelogram…

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Q: In R³, consider the triangle formed by X (2,0, 4), Y (0,5, 0) and Z (-2,0,0). Us- ing vector and…

A: Let's find.

Q: The distance from (-3,-4,-7) to the yz-plane is (A) -4 (B) 4 (C) -3 (D) 3 (E) 7

A: The distance(d) between two points (x1,y1,z1) and (x2,y2,z2) in a cartesian coordinate system is…

Q: Find the area of the parallelogram defined by the vectors Area = 1 -2 2

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Q: ? (2,3), (0,0) }

A: Let S=2, 3, 0, 0. We need to find whether the set S spans a line or all of ℝ2.

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

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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: 24 Resolveu = [8, 3, 5] into rectangular components, one of which is collinear with v = [3, 1, 2].

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Q: Which point(s) lie in the plane 2x + 3y + 4z = 24? a) (0, 0, 6) c) (4, 4, 1) b) (0, 3, 4) d) (-2, 6,…

A: Given: 2x+3y+4z=24 For finding which point lie on given equation of plane, we put each point on…