D1.3. 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; (b) RAC: (c) the angle OBAC at vertex A; (d) the (vector) projection of RAB on RAC-

Q: Q2. Use a scalar product the check whether the points A (0, 4, 1), B(2, 3, -1), C(4, 5, 0) and D(2,…

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Q: Let C = (1,–3, 2) and D = (-1, 2, – 3, ). Find the following. (a) The cosine of the angle between D…

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Q: The vertices of a rectangle are R(-5,-5), S(-1, -5), T(-1, 1) and U(-5, 1). After translation, R' is…

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Q: Write the vector equation of the line defined by the following points. (25,17,42)and(-16, 12, 25)

A: Answer is given below :-Explanation:To find the vector equation of the line passing through two…

Q: Let T: R2 R be a reflection in the x-axis. Find the image of each vector. (a) (7, 6) (b) (9,-3) (c)…

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Q: Find the angle between the two planes. The first plane contains the points A(1,2,3), B(6,3,2),…

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Q: What vector v is given by the coordinate vector B = { 9x +4, 4x + 6 }. [3] ? B

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Q: Evaluate (6x-3y)dA where Ris the parallelogram with vertices (2,0), (5,3), (6,7) and (3,4)using the…

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Q: 7. Let z = -3 + 5i. Plot the points z,-z,7,-ž and - in the complex plane.

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Q: What are the projections of the point (−2, 3, 4) on the xy-, xz-, and yz-planes? Draw a picture and…

A: Given, the point (-2, 3, 4), we have to find the projections of this point on the xy-, yz-, and…

Q: The plane II contains the points (1,2,3), (0.1.2) and (2,3,0). The line L passes through the points…

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Q: 13. Prove that the three points (-3, 2, 4), (6, 1, 2), and (-12, 3, 6) are collinear by using the…

A: To solve the following problem

Q: A parallelogram is formed by the vectors a = (1, 0, -1) and b = (2, 1, 1). What is the area of the…

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Q: R = 2Ã – 3B + Č Figure 1 (c) Three vectors A, B and C are shown in the figure 1. Represent the…

A: parallelogram law states that if two vectors are initiated from one point then the diagonal starting…

Q: Place the vectors a, b, c, and d in order of length, from smallest to largest. Show your…

A: We have to find length of each vectors first.

Q: 3. Given two points P(4,0,2) and Q(2,-1,3), find the equations of the vector PQ, the line passing…

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Q: Find k so that the points P(0, 1, 1), Q(-1, 1, 3), and R(-3, 1, k) are on the same line (collinear).

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Q: T: R R be a reflection in the x-axis. Find the image of each vector (a) (7, 6) (b) (9,-3) (c) (-a,…

A: Given vectors are d) (0, b) e) (-c, d) f) (f, -g) We have to find the reflection in x-axis

Q: Calculate the dot product of ?=(−4,−2,7,−3)and ?=(−3,1,5,8)

A: Given vector is u→=−4,−2,7,−3 and v→=−3,1,5,8. We have to calculate the u→⋅v→.…

Q: Find x such that the points A(x, 5), B(2, 3), and C(4, - 5) are collinear.

A: Given. A(x,5), B(2,3) and C(4,-5) are collinear.

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.