The four points A, B, C, D have position vectors pi, j+qk, k and i+j respectively, where p and q are positive real numbers. Find vector equations for the lines AB and CD.

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Q: find the component form of the vector. The sum of AB and CD, where A = (1, -1), B = (2, 0), C = (-1,…

A: Given that A = (1, -1), B = (2, 0), C = (-1, 3), and D = (-2, 2)We have to find AB + CD.

Q: For the pair of vectors find 2U-3V

A: U=6, 6V=6, -62U=26, 6      =2×6, 2×6      =12, 12

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Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

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A: Solution as given below:

Q: Given the points A: (-4,6,2) and B: (-1,5,-3), find the vector ū AB

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Q: Consider the points P(2,7) and Q(6, 4). Write PQ as a product of its magnitude and a unit vector in…

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Q: find a. the direction of vector P1P2 and b. the midpointof line segment P1 P2. If vector AB = i + 4j…

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Q: B) find a vector that is parallel to the line whose equation is : 4-x 3-6z % = 3 – 3y = 5 9

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A: To find- vector u.

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Q: Given initial point P1 = (6, 6) and terminal point P2 = (−6, 6), write the vector v in terms…

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Q: = Find the vector equation for the line passing through the points P₁ P₂ = (2,7-13). (5,-1,-5) and

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Q: Find a position vector that is parallel to the line x = 2 + 4t, y = 5 - 8t, z = 9t.

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A: Given: The position vector of the points 5i^-4j^ and -3i^+4j^; -13i^+4j^ and -5i^+j^

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Q: Find a vector equation of the line that passes through A(5,-4) and B(1,-1)

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Q: value

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Logic and Proofs

Discrete mathematics deals with the separated values of data such as integers. It is widely used in the practical field of computer science and mathematics. By knowing discrete mathematics one can improve their reasoning and problem-solving capabilities. Discrete mathematics became popular after the boom of computers which operate in discrete steps and store data in discrete bits. It also useful in studying computer programming, algorithms, and cryptography.