a. Find a nonzero vector orthogonal to the plane through the points P, Q, and R, and b. find the area of triangle PQR. 29. P (1, 0, 1), Q(-2, 1, 3), R(4, 2, 5) Answer +

Q: Which of the following vectors is parallel to the line 7x+ 14y = 20? %3D (-6,3) (8,-16) (2,4) 0.…

A: We first find the slope of the line using y=mx+b form

Q: What should the value of y be for the given vectors å = 3î + 2ĵ + 2k , b = î - ĵ +k and ĉ = 2î + 2yj…

A: Given that three vectors are in the same plane or we can say the vectors are coplanar. If three…

Q: a) Find the vector that is parallel to the tanget to the circle x2 +y? = 100 at the point (3,4).

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Q: For the vector a,b,c ∈ IR3 a+b+c=0 and ===1 then ?

A: We will first assume a=(a_1,a_2,a_3),b=(b_1,b_2,b_3) and c=(c_1,c_2,c_3).Now will will use…

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: #1. The area of the parallelogram spanned by the vectors v = (A) – 22 (B) 22 (C) 23 (D) 8 (E) 2 (5,…

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Q: For what value of m, the vector 4i + 2j – 3k and mi - j+ 3k have same magnitude? Given the points A…

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Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

A: topic - point and vector parallel to line

Q: 4. Let Ā = -(1+ m)î + 7j – 5k ,B = xî + (6 + n)j – 2k and C = (8+ m)î – 2k , find the following:…

A: Given data is : A→=-1+mi+7j-5kB→=xi+6+nj-2kC→=8+mi-2k

Q: 2. Use the given equation of a line to find a point on the line and a vector parallel to the line.…

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Q: Find all values of h such that the vectors {a,, az} span R?, where a1 a2

A: Given that,

Q: Q. 6: Suppose the sides of polygon represent vector arranged head to tail. Calculate the sum of…

A: Given: the sides of polygon represent vectors arranged from head to tail. To calculate: the sum of…

Q: What angle does the line of intersection of the planes (x 2y + 3z 5 and 4x+y-2z-7 make with the…

A: The dot product of two vectors u→, v→ is calculated using the formula: u→·v→=u→v→cosθ, where θ is…

Q: Find the value of z of vector A= 3i +3j+ zk if ß = 59.04° and y = 46.686° %3D

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Q: Determine the value of m and n so that the vector ?⃗ = (2, 4, 6) is perpendicular to both the…

A: To find: The value of m and n. Given: The vector 2,4,6 is perpendicular to m,n,10 and 6,m,n. Concept…

Q: 3a) Use the cross product to determine a unit vector that is perpendicular and in the opposite…

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Q: Perform the indicated operations for the given vector. v = ⟨8, −10⟩ w = ⟨−3, 7⟩…

A: The explanation of answer as follows

Q: 16. The accompanying figure shows nonzero vectors v, w, and z, with z orthogonal to the line L, and…

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Q: Which of the following vectors are parallel to v = (6, 9) and whichpoint in the same direction? (12,…

A: Solution:Given     v=(6,9)To find the vector are parellel to v and point in the same direction.

Q: Below is a diagram of the dotted cube with edges of length 3. Suppose vectors u = (3,0, 0), v = (0,…

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Q: a. Which translation vector represents the path of the ball from T tol DC? DC? b. What translation…

A: GIVEN :

Q: Given the vectors vi = (1,1, –1), v2 = (1,2,3) and v3 = (0,1,1). S = { v1, v2, v3} set R3 does it…

A: 3 vectors span R³ if they are linearly Independent. Vectors are linearly Independent if their…

Q: 41. For what values of t are the following pairs of vectors parallel? (a) 27 + (r² + 71 + 1)j +ik,…

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Q: Given that the vectors a=(6,-1,2k)  and b=(-1,k+1,4) are perpendicular, what is the value of k?

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Q: 7. Find the values of m that will make the following vectors perpendicular. à = (2m, 3,1), b = (m,…

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Q: Given perpendicular vectors a = (5,3,-1) and 6=(2,2,k), find ||||.

A: Given perpendicular vectors a→=5, 3, -1,     b→=2, 2, k   To Find: b→

Q: Determine the dot product a) Ā = and B = b) Á = and B c) Á = 5, ||B = 32 and the angle between the…

A: (a) Given that A→=<9,4,-5> and B→=<3,-2,7>

Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+fk where a = 3, b = -3, c =…

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Q: Define the points P(2,-2) and Q(3, 4). Carry out the following calculation. Find two vectors…

A: Solve the following

Q: For the triangle with vertices located at A(5,3,5), B(2,4,4), and C(1,1,1), find a vector from…

A: The midpoint of AB is obtained by taking the average of the coordinates of the points A,B.

Q: Given the vector component of D(2, − 6, − 5) and G(1, 2, 3), find the vector of D that is parallel…

A: Given:      D2,-6,-5       G1,2,3 Two vectors D and G are said to be parallel if their cross product…

Q: Q/ B/ If vector A = 3i – 2j + 7k and B = -i+j- 3k , find the area of triangular between vector A and…

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Q: (1) Let 0 be the angle between vectors A and B, find the value of the angle 0 when |-5V3A x B = 5Ã.B

A: To find the angle θ between vectors A and B. It is given that,

Q: Let Ā = -(1+ m)î + 7j – 5k , B = xî + (6 + n)j – 2k and Ĉ = (8+ m)î – 2k , find the following: If…

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: For what values of b are the vectors (–88, 6, 7) and (b, b², b) orthogonal? Answer (separate with…

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Q: Given the vector component of D(2, – 6, - 5) and G(1,2,3), find the vector of D that is parallel to…

A: Given vectors D(2, -6, -5) and G(1, 2, 3) We need to find the vector of D that is parallel to G

Q: Given vectors ū = [x, y,5] , i = [3,1, –4], and w = [7,7,7] , find x and y such that u xi = w. Тext

A: given,       u⇀=x,y,5   ,   v⇀=3,1,-4   and   w⇀=7,7,7

Q: 4) Which of the following vectors is parallel to the line L: x = 1 -t, y = 2 + 3t, z = 5 + 2t? a)…

A: According to the guidelines we are answering first question. Please repost the remaining.…

Q: Suppose that A= 2i + j, B= i – 4j + k, and Ĉ =j+k. What is the direction of vector A? A A. 26.6 E of…

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Q: 8. ABCDEF is a regular hexagon with AB, representing the vector m and AF, the vector n. Find the…

A: Given that: AB→ is representing the vector m and AF→ is representing vector n.

Q: Given the points P(4, 4, 3), P(1, 4,0) and P3(10,0, 2). Find the vector that is orthogonal…

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Q: Find the angles that vector D 2.5 - 8.5 + k) m makes with the x-, y-, and z- axes.

A: Follow the procedure given below.

Q: Calculate the slope m of the following vectors and / or line segments in a plane (can be complex) a)…

A: Topic - slope of vector and line Note : As per bartleby guidelines,we are supposed to answer only…

Q: 3- Given a vector A (r 17.5, 0= 90°, o = 55") and vector B (r=17.5, 0= 40°, q = 55") the distance…

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Q: Below is a diagram of the dotted cube with edges of leng Suppose vectors u = (3,0, 0), v = w =…

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Q: Find the area of the parallelogram with the vertices A(3; 2), B(5; 4), C(4; 1). (Advice: Consider…

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Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: Which vector is not a linear combination of x, y and z? 2 X = 1 y = z = 1 -2

A: Given: x=21-1 ,y=101,z=11-2 Let's check all option  (i) 0-13 Let's choose scalars 0,1,-1, then…

Q: Which of the following planes are parallel to the vector (4, 1,-5)? Select one or more: O a. 6x + y…

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