By vector methods, show that the line segment joining the midpoints of two sides of a triangle is parallel to the third side, and has length equal to one half the length of the third side.

Q: Define the term Parallel Vectors?

A: Parallel vectors: The vectors that are parallel if they have the same direction.

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: A vector with magnitude 7 points in a direction 145 degrees counterclockwise from the positive x…

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Q: If vector a= and vector b=, find the angle between vectors a and b, rounded to the nearest degree.

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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: Consider the parallelogram given by vectors [12, 5], and [18, 0]. Give the lengths of the altitudes…

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Q: If a vector gets multiplied by a positive number, its direction will be *.reversed FO TO

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Q: Use vectors to show that the distance from P1(x1, y1) to the line ax + by = c is d = |ax1 + by1 -…

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Q: Find a vector equation for the line segment that joins P(1,3,4) to Q(-2,4,6)

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Q: The path C to D is consistent with what unit vector and its sign? The path G to C is consistent with…

A: Given:  To find the unit vector for the following paths for which they are consistent and the sign…

Q: Find the vector of length 2 making an angle of 60° with the x-axis.

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Q: The unit vector in 2-space that makes an angle of π/3 with the positive x-axis is _____

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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: B. Explain with sketch how can calculate the volume of parallelepiped by three vectors?

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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: Find the area of the parallelogram that has the vectors as adjacent sides. u- (3, -5, 3) v = (2, 0,…

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Q: If vector v is represented by an arrow, how is -3v represented?

A: Given: If vector v is represented by an arrow. To find: How is -3v represented?

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: photo is attached

A: Given informationVector V = (-3, 5)

Q: What is the magnitude of the cross product of two parallel vectors?

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Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: Which vectors, drawn on a grid from one point (on the "cross-hairs") to another have integer values?

A: Y-component of A →…

Q: We define a median vector of a triangle to be the vector from a vertex of the triangle to the…

A: Let ,The triangle be ∆ABC A(x1, y1, z1)B(x2, y2, z2)C(x3, y3, z3)AM→ , BM→ , CM→ be the medians

Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

A: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

Q: Use vectors to prove that the line segment joining the midpoints of two sides of a triangle is…

A: Using Vectors, Our Aim is to prove that the line segment joining the midpoints of two sides of a…

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: Use vectors to prove that the line connecting the midpoints of two sides of a triangle is parallel…

A: Let the arbitrary triangle has vertices A, B and C has three vectors AB, →AC →  and  BC → . Let M…

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

Q: Find the angle between the vectors (2, 1) and (3, -2) to the neareast second.

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Q: five vectors in Span v1, V2}. Do not make a sketch. 8 - -

A: In this question, the concept of the span of the vector is applied. Span The smallest linear…

Q: he vector as a

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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: Express the vectors in terms of their lengths anddirections. -i - j

A: Given vector is: v = -i -j Then we get, The magnitude or the length is: = sqrt{(-1)^2+(-1)^2} =…

Q: Explain how to find a vector in the direction of the line segment from P0(x0, y0, z0) to P1(x1, y1,…

A: Initial point is P0x0, y0, z0 and the terminal point is P1x1, y1, z1.

Q: Find the vector of length 2 making an angle of 45° with the x-axis.

A: Find the vector from the given data

Q: Use vectors to prove that the line joining the midpoints of two sides of a triangle is parallel to…

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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: The sum of two vectors is called the ___________, and it can be represented geo-metrically as the…

A: The sum of two vectors is called the resultant, and it can be represented geometrically as the…

Q: Vector ä has a magnitude of zo and poin ts 60' Norte of East. Caleulate the * and comporents of À

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Q: Show that direction vectors of the lines L: and are arthogonal.

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Q: Please state the Pythagorean Theorem using the language of vectors; then prove it.

A: In this given question ask state of pythagorean theorem using the language of vectors and prove it.…

Q: If a vector v lies in the third quadrant and makes an angle n with the positivex - axis and…

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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: What are parallel vectors?

A: We have to define parallel vectors. Two vectors are said to be parallel if they have same direction…

Matrices

‘Matrices’ is the plural form of the word matrix, and it is basically a spreadsheet in the form of a box. In mathematics, various functions can be carried out with matrices. Generally, a matrix comes in the shape of a square or rectangle. The elements are distributed horizontally in the form of rows, and vertically in the form of columns.