1. Graph the vectors a) (-3,0,0) Axis? b) (0,5.0) Axis? --

Q: Given a line 2a + y = 2 in the two-dimensional plane, • If a given point (a, 3) satisfies 2a + B >…

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Q: Given the points P, Q, and R, how do we know that the vectors PQ (cross product) PR is perpendicular…

A: Given that there are three pints in the plain P,Q and R.The cross product between PQ and PR is…

Q: or what values of aj are the vectors [ai,4,3] and a) orthogonal? b) Parallel? c) Have 45 degree…

A: If 2 vectors a⇀,b⇀  are orthogonal, their dot product a⇀.b⇀ =0 Let u=a1,4,3 and v= 3,-2,12 So,…

Q: If the magnitude of vector x is 10, y is 21 and magnitude of x-y is 17 what would x+y be?

A: Use the property of magnitudes to solve this problem.

Q: 10. In the figure here, D is the midpoint of side AB of triangle ABC, and E is one-third of the way…

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Q: In triangle ABC a line is drawn from A to the midpoint of BC, labelled D. Prove that vectors…

A: The solution is given by using triangle law of vectors as follows

Q: 4 9. is 6/2 The distance between the vectors u = and y = -2 %3D -5 True O False

A: Suppose u and v be any vectors from a same vector space. Then the distance between u and v is…

Q: When two nonzero vectors w are called perpendicular or orthogonal?

A: Let two nonzero vectors are u and v Then the scalar product of the two vectors is given as,…

Q: 33. If 0 is the angle between two nonzero vectors v and w, and v· w < 0, what is the range of 0?…

A: Use the geometric definition of the dot product to calculate the angle between two non        zero…

Q: 3 Give the position vectors of A, B, C, D and E relative to O for the diagram below. B D-

A: In geometry a position vector so known as location vector. Here we find position vector relative to…

Q: if vector AB=i+7j-4k and B is the point (9,3,5) find A

A: Let A=ai^+bj^+ck^B=di^+ej^+fk^ be twovectors.Then AB→=d-ai^+e-bj^+l-ck^

Q: α, β and γ are the angles made by the vector with x, y and z axis respectively. The squares of the…

A: Given ,  α, β and γ are the angles made by the vector with x, y and z axisrespectively. We have to…

Q: Given three vectors, u, v, and w, if u (v x w) = 0, what geometrical result can be concluded?

A: We have to conclude the result of u→.(v→×w)=0→.

Q: What is the area of the parallelogram formed by the vectors v = (1,0, 1) and w = (0, 2, 2) tail to…

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: When do directed line segments in the plane represent the same vector?

A: Vectors are represented by the line segments in which the length of the line segment is called the…

Q: The angle between the vectors A = 17- 31+4 k and B= 5î -3ĵ+0 k, in term of cose is Answer:

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Q: What is the angle of vectors A=5m West and B=15m 60° North of West?

A: The vector A can be written as: a=-5i The vector B is 60 degree north of west that means it makes an…

Q: Show that the points with position vectors 3i−5j, 4i+j, 6i+13j are collinear. If the point whose…

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Q: If vector AB = i + 4j - 2k and B is the point (5, 1, 3), find A.

A: Given,

Q: ABC is a triangle and P, Q are the midpoints of AB, AC respectively. If AB = 2x and AC = 2y, express…

A: Given P,Q are the mid-points of 2 sides AB,AC of the triangle ABC. Also, AB=2x, AC=2y.

Q: The area of a parallelopiped that is formed by two vectors A and B can be obtained mathematically…

A: It's area of parallelopiped is given by A×B.

Q: Solve for the projection of the vector P = (3,4, 4) onto Q = (0, –2, –5). What is the exact measure…

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Q: What is the angle e between the vectors u= and v= in R* ? (Express the answer to the nearest…

A: B

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

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Q: 2. Consider the two vectors a and b, as graphed below. 2a Plot the result of a +b on the same axes.…

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Q: Show that the vector v = ai + bj is perpendicular to the line

A: GivenVector V = ai + bj and the line ax + by + c

Q: 3. Prove by using vectors that the points P(-2,1,6), Q(2,4, 5), and R(-1,–2,1) are he vertices of a…

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Q: What is the angle of vectors A=5m South and B=15m 60° South of West?

A: `Vector is a quantity that has magnitude as well as direction. So we need to find the angle of…

Q: Is the vector ?⃗ = ⟨−1, −2, 3⟩ perpendicular to the plane 3? + 6? − 9? + 5 = 0? Please give full…

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Q: Given that the vectors ở = (1, 2– k,3) and b = (7, 4, k+2) are perpendicular, what is the value of…

A: Given vectors are: a→=1,2-k,3 and b→=7,4,k+2

Q: Given the vectors a=(1,2,3) and b=(1,−1,2), what is the dot product a⋅b⋅a?

A: Solution :- let a = (x1, y1, z1) and    b = (x2, y2, z2)  be any two vectors then their dot product…

Q: 4. Determine the resultant of each combination of vectors. a. 25 km/h north and 81 km/h east b. 12 N…

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Q: Find a vector equation with parameter ?t for the line through the point (8,0,−5) and parallel to the…

A: Given,           The line through the point (8,0,−5) and parallel to the vector 2i−3j+3k

Q: For what value(s) of a is the angle between the vectors ⟨4, 1+ 2a, 4⟩ and ⟨1, 4, 4 − a⟩ obtuse?

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Q: 2a.) Suppose u, w are two vectors in R7 satisfying uxu 4, wxw 16, uXw = 8, What is the cosine of the…

A: We are given that : u→.u→=4⇒u→u→cos 0=4⇒u→2=4⇒u→=2 w→.w→=16⇒w→w→cos 0=16⇒w→2=16⇒w→=4 Now, Let θ be…

Q: Find the measures of the angles of the triangle whose vertices are A = * .(-1, 0), B = (2, 1), and C…

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Q: Which vector is not collinear with [c, d]? O [2c, 2d] O(-c, -d] O [10c, 10d] O [d, c]

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Q: For what value(s) of k are the vectors ü (2k, 5, k) and v = (3, -8, k) perpendicular

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Q: ABC is a triangle. If D is the midpoint of AC, show that BA + BC = 2BD. Vectors

A: Consider the given information. Let's draw the triangle.

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: 4 3 Which weights should be used for b = a, vị + a2 V2 to obtain the vector b = ? 2 a1 = Ex: 42 az =

A: Solve the following

Q: Suppose i and V are vectors such that ||ū|| = 2, |||| = 3, and the angle between u and ở is 60º. a)…

A: This question is related to vectors, we will use formula of dot product of vectors and basic…

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

Q: 6. Show that the points A, B and C with position vectors d = 32 – 4) – 4k, b = 2î – ĵ + k and & = î…

A: To show that the points A,B and C with a given position vectors forms a right angled triangle.

Q: see attachment

A: We have to use dot product formula.

Q: Show that the points with position vectors 3i–5j, 4¿+j, 6¿+13j are collinear. If the point whose…

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Q: 2. The diagram below was created using equilateral triangles congruent to ABSR. If OS=ā and OT=b),…

A: The given figure is:

Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

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