The three vertices of a triangle are located at A(6, –1, 2), B(-2,3,-4), and C(-3,1,5). Find: (a) RAB X RAC? (b) the area of the triangle? (c) a unit vector perpendicular to the plane in which the triangle is located.

Q: How do you find the dot product a. bof two vectors if you know their lengths and the angle between…

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Q: Find a vector equation for the line through the point (-6, 4, 1) perpendicular to the vectors u =…

A: A line passes through the point -6,4,1 and perpendicular to the vectors u→=-1,-2,3 and v→=3,-8,-9 We…

Q: Determine the resultant of two vectors with magnitudes of 50 and 30 and an angle of 110 degrees…

A: let  A=50 & B=30, θ=1100 We know resultant between two vectors A→ & B→ when angle between…

Q: In Cartesian coordinates, the position vector at point (3, 40, 1) is represented by

A:

Q: Find equations for the planes The plane through A(1, -2, 1) perpendicular to the vector from the…

A: The normal vector of the plane is given by A(1,-2,1)  The point of passing is (0,0,0). The equation…

Q: What is the terminal point of the vector a = <1, 3> based at P = (2, 2)? Sketch a and the…

A: Consider the provided information, The component vector v=PQ→ where P=a1,b1 and Q=a2,b2 are…

Q: In a standard coordinate system, the unit vectors in the three main directions are orthogonal to…

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Q: Write three properties of parallel vectors p and q.

A: Introduction: Only when there is a 0 degree angle between two vectors can it be said that they are…

Q: B) Find a vector perpendicular to the plane of P(1, 4, 4), Q(2, 4, 5), and R(-3, 4, 0). Which axis…

A: See the attachment

Q: Given points (-1, 5, 3), (3, -2, 4), and (-1, –3, 2). compute the area of the triangle they…

A: * A,B,C are points then unit vector is →AB×→ACII→AB×→ACIIand area oftringle is 12→IAB×→ACI

Q: Find the angle between the vectors a=(2,2,-1) and b=(5,-2,3)

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Q: photo attached

A: Given point can be written in vector form as,

Q: A parallelogram is determined by the vectors = (-2, 5) and 7= (3, 2). Determine the angle between…

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Q: Prove using vectors that the points (1,1,2)A(2,1,1), B(1,2,1), C represent the vertices of a…

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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: If A is (3,5,0), B is (-1,-2,7), and C(6,1,3) forms a triangle. Find the vector component of CB…

A: let a,b,c are position vector of point A,B,C respectively. Therefore a=3i+5j, b=-i-2j+7k c=6i+j+3k…

Q: Do the vectors (1, 0, 0), (0, 1, 0), and (2, 3, 0) lie on the same plane? Briefly explain how you…

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Q: photo attached

A: Given that a vector V goes from the origin to a point (5, -5).

Q: What is the vector between the point (−3a,−7b) and the point (−4a,−5b)?

A: Vector between two points A and B is B-A

Q: The points A, B, C and D form a parallelogram. The points A, B and C have position vectors 2i –…

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Q: Find an equation of the plane through the point and perpendicular to the given vector. (8, 2, 3)…

A: We will find an equation of the plane through the point (8,2,3) and perpendicular to the given…

Q: Consider the vectors ū = (1,–3, -5) and i = (1,4,–10) and 0, the angle between them. Find 0

A: Given vectors are u⇀=1, -3, -5 and v⇀=1, 4, -10. To find angle θ between them. Solution: We know…

Q: The unit vectors normal to the vectors (2, - 8,11) and (- 3,0,5) are

A: Find unit vector

Q: Find the vector from the origin to the point of intersection of the medians of the triangle whose…

A: To determine the point of intersection of the medians of the triangle.

Q: Find the equation of the plane containing the point ( – 5, – 10, 9) and the two vectors and -

A: Given that , Plane containing the point -5,-10,9 So , a→=-5 i^-10 j^+9 k^ And vectors are ,…

Q: How long is the shadow cast by a 540-foot tower when the sun's rays follow the vector [6,10,-27]?…

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Q: A figure is translated using the vector (-3, 7). What translation vector would move the image back…

A: i have provided solution in step2

Q: b) How do you tell if two vectors are perpendicular?

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Q: Show that the pair of vectors is perpendicular. 3? + ? and ? − 3?

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Q: (a) How do you tell if two vectors are parallel?

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Q: Calculate the values of a and b so that points A (1,1,1), B( a,2,b) and C(1.0,0) are aligned…

A: If two vector are collinear , then they are scalar multiple of each other. that is AB→=λAC let a ,…

Q: Find a unit vector u in the direction opposite of (-8,-4,-3).

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Q: Find the acute angle formed by two diagonals of a cube. (vectors) show complete solution.

A: It has been assumed that the length of each side of the cube is a unit.

Q: Find an equation of the plane through the point (29,-37,46) and with normal vector 14i+19j–17k.

A: we have to find an equation of the plane passing through the point (29,-37,46) and with normal…

Q: Find an equation of the plane that passes through the given point and is perpendicular to the given…

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Q: Find the measure of the angle between the two vectors. (-4, 5) (-6,3) ►

A: Consider the graph

Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

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Q: Find a unit vector perpendicular to the plane ABC if A (2,-2,1), B (3,-1,2) and C (3,-1,1)?

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Q: Find the volurne of the parallelepiped determined by the vectors a, b, and c. a = (6, 3, -2), b =…

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Q: Use vectors to decide whether the triangle with vertices P(1,-3,-2), Q(2,0,–4) and R(6,–2,-5) is…

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Q: Find the angle between the vectors. a=(3, 4, – 2), b=(0,1,2)

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Q: What is the equation of the vector in a Cartesian coordinate system that originates from the origin…

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Q: Use vectors to show that the triangle with vertices (-2, 2), (4, 10), and (20, –2) is a right…

A: vector method to find right angle triangle.

Q: Find the vector equation of the line (d) through (6, −3) and parallel to the line through (5, −1)…

A: First, we find the slope of the line  through (5, −1) and (2, 11) Direction vector is=(2, 11)-(5,…

Q: ū = (-2, -12, 4), ₺ = (3, -2, 1).

A: Here we use the vector addition formula.

Q: Find the area of the parallelogram that has the vectors u = (2, -1, 5) and v = (3, -4, 1) as…

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Q: If a vector V is in standard position and the tip of the vector corresponds to the point(a, b), then…

A: Given, If a vector V is in standard position and the tip of the vector corresponds to the point(a,…

Q: Find an equation of a plane passing through the given point and perpendicular to the given vector.…

A: The equation of the plane perpendicular to the vector <a, b, c> is: ax+by+cz+d=0 Therefore,…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.