Let a =)33) A) Find the eavution of the Plane which has a a nomal vector t conthins Point 3,3) Find unit vector w Same direction as a,

Q: In Exercises 15-18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: Answer

Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: The volume of the parallelepiped determined by the vectors a =,b = and c = is: (A) 12 (B) 6 (C) 24…

A: The given vectors are a→=3,4,5, b→=2,1,-1 and c→=3,2,1

Q: Prove the stated property of distance between vectors. d(u, v) = d(v, u) for all vectors u and v

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Q: Prove the stated property of distance between vectors.d(u, v) = d(v, u) for all vectors u and v

A: Given the stated property d(u, v) = d(v, u). We need to prove the above stated property.

Q: Find a formula for the projection of any given vector w onto the plane u · x = 0 in R', where u is a…

A: The objective is to find the formula for the projection of any given vector w onto the plane u.x=o…

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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Q: Consider the two vectors A = A,i + Ayj and B = B,î + Byj. In cross product, %3D %3D ixî = j xj = 0,…

A: We have given two vectors A→=Axi^+Ayj^  and  B→=Bxi^+Byj^ i^×i^=j^×j^=0i^×j^=k^, j^×i^=-k^   Find…

Q: Find the area of the parallelogram spanned by vectors v and w suchthat ||v||=||w|| = 2 and v · w =…

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Q: IF A =2âx+4ây , B =-3âx+âz and C =2ây+3âz, the vector in the plane containing A and C and…

A: Given: Let us consider the given values as ,  A→,B→,C→A→=2a^x+4a^yB→=3a^x+a^zC→=2a^y+3a^z

Q: Prove the stated property of distance between vectors. d(u, w) <= d(u, v) + d(v, w) for all…

A: We have to prove the property of distance between vectors as,

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The area of the parallelogram determined by the vectors u and v is A=u×v. Given u = i + j and v = j.…

Q: / If A(1,23=1), B(3)6-7), C(233,-3),D(34-3), Cal culate the angle between the vector Projection of…

A: If vector a→ is projected on vector b→ the the formula of vector projection will be…

Q: Find the area of the parallelogram that has the following vectors as adjacent sides. u = & v =

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Q: Use the dot product to find the angle between the vectors v =i – 2j + k and w = i+j-2k. For which…

A: First we have to find the angle between the vectors v and w where v=i-2j+k and w=i+j-2k. For this,…

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: The volume of the parallelepiped determined by the vectors a =,b = and = is: (A) 12 (B) (C) 24 (D)…

A: Volume of parallelopiped

Q: (a) Prove that the planes 4.x – 2y + 6 = 0 and y – 4z – 13 = 0 intersect each other. (b) Find the…

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Q: Prove the stated property of distance between vectors. d(u, v) = 0 if and only if u = v

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Q: 19. What is the radius vector of the point on the terminal side of an angle in standard position if…

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Q: Let P be the plane in space that intersects the x-axis at 5, the y-axis at −5, and the z-axis at 4.…

A: Given query is to find the perpendicular vector to the plane p.

Q: find (a) the area of the parallelogram determinedby vectors u and v and (b) the volume of the…

A: The vectors u, v, and w. u=i+j-k,v=2i+j+k,w=-i-2j+3k.

Q: Triangles in Space

A: Area of triangle formed by P,Q,R is given by  Area=PQ ⇀×PR⇀2 UNIT VECTOR is given by  unit vector=PQ…

Q: Q. For the Spheri cal polas Coozdinates (r0,d), prove that their unit vectors mutually orthogonal?…

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Q: e) Four non-coplanar points A, B, C, D are positioned such that the line AB is perpendicular to CD,…

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Q: Determine the angle between the two vectors: x = ai+bj+ck and y = di+ej+k where a = 2, b = 5, c = 1,…

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Q: Prove that ? is parallel to vector ? using scaler product if ⃗̂̂ ?=−3?̂+4?̂−? ,?=−9?̂+12?̂−3?

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Q: The area of the parallelogram whose adjacent sides are the vectors u and v is a) Ju · v| c) Ju x v|…

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Q: Exercise 1:If 0 is the angle between vectors a and b, show that projab. projpa = (a.b) cos (0) COS

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Q: In Exercises 15–18, a. Find the area of the triangle determined by the points P, Q, and R. b. Find a…

A: We'll answer the first question since the exact one wasn't specified . Please submit a new question…

Q: 1Triangte with points (2.0r-)ornd R(or2 find -Ared of the iangle 7 vector PerPend teular to 2 AUnit…

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Q: Suppose that n is normal to a plane and that v is parallel to the plane. Describe how you would find…

A: Consider the given information as n is normal to a plane and that v is parallel to theplane.

Q: Find the projection of the vector v onto the vector w if v = 2i + j and w = 6i + 3j

A: we have given v and w vectors . We have to find the projection of the vector v onto the vector w

Q: Verify the parallelogram law for vectors u and v in R": |u + v|l? + ||u – v||° = 2||u||? + 2||v||?

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Q: Find the volume of the parallelepiped determined by the vectors a i+2j-k, b 3i+j-4k and e= -2j+5k. O…

A: The parallelepiped is formed by the vectors, a→= i + 2 j - kb→= 3 i + j - 4 kc→= -2 j + 5 k  volume…

Q: Let a 5? ER be vectors, Using ouly vector geome trk dechaiqnes, frove thaf geenne (+)+ご + で+) 07

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Q: Given the vector vec u = langle-6,-3 rangle , find the magnitude and angle in which the vector…

A: magnitude of x =x2+y2

Q: Prove the stated property of distance between vectors.d(u, w) < d(u, v) + d(v, w) for all vectors…

A: Basic logic and properties of vectors can be used to solve the question.

Q: e part of the plane with vector equation r(u, v) = (4 + v, u – 3v

A: Here we have to find the area of the part of the plane with vector equation r(u,v)=4+v, u-3v,5-4u+v…

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: Imagine that you are at the center of the ground of a pyramid, whose base is a regular hexagon with…

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Q: Let P be a plane in R3 given in vector form by -> x = td + sd, +p and l be a line in R3 given in…

A: Given that D:x=td1+3d2+p is the plane passing through the point whose position vector is P and…

Q: Which polygon is the result of reflecting polygon 1 through AB, then translating the reflected…

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Q: The volume of the parallelepiped determined by the vectors à =,b= and = is: %3D (A) 12 (B) 6 (C) 24…

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Q: Determine two unit vectors, vand wl, perpendicular to the plane passing through the z-axis and point…

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Q: Find the signed volume of the slanted box in R" generated by the vectors 27 11 3 vi = 6. V3 = ,V4 =…

A: Given that, v1=0263,v2=-2-1-10,v3=-1-203,v4=-13-20

Q: perpendicular to the plane formed by the vectors w1 = [1 2 1] and w2 = [2 2 3], with the z axis

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Q: Give a vector description of the midpoint M of a line segment AB→.

A: GivenLine segment AB→To find vector description of midpoint of AB

Q: Express in Cartesian components: (a) the vector at A(4, 40°, -2) that extends to B(5, -110°,2); (b)…

A: express in cartesian components (a) the vector at A4,40°, -2 that extends to B5,-110° , 2 (b) a unit…

Q: Draw a diagram to illustrate point R divides line PQ such that PR=RQ and R is the midpoint of PQ,…

A: Concept: Vector: A vector is a -dimensional entity with significance and course. A vector may be…