Which of the following points (given by Let / be the line through the point with coordinates (-1,-1,1) in the direction of the vector -1 their coordinates) lie on /?

Q: be the line through the point with coordinates (0,1,0) in the direction of the vector h of the…

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Q: 2. Find the angle between vector [2, -5,7] and vector [6,4,1]

A: Vector [2,-5,7] and vector [6,4,1]  We have to find angle between these two vectors

Q: Let 2 = (-8,1) and To (-7, -2) Compute the following vector B Prijz To projections.

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Q: 5. (a) Given A = a,5-ay2 + a₂, find the expression of a unit vector of B such that B/A and BL A, if…

A: Solution 5(a): Given that A→=5ax-2ay+az and  B→∥A→ if B→ lies in the xy-plane. So, B→=5bx-2by. Unit…

Q: a line is parallel to the vector i+ 5j+3k and passes through the point P = (6, 2, 4), then the…

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Q: Which of the follow is the direction vector of the line 7=(2, 1, 3) + t(-7, 1, 6) (7, 1, 6) O(-7, 1,…

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Q: 5. In each case, find the equation of the line with the given properties. (a) Passing through the…

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Q: Let L be the line with parametric equations x-2-2t y-10-2t 2-8-21 Find the vector equation for a…

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Q: Let P(-1, 1, 3) and Q(-3, 1, 5) be points in R3. Find the components, magnitude and direction angles…

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Q: Let / be the line through the point with coordinates (1,-1,0) in the direction of the vector…

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Q: 5. Determine a vector equation of the line that passes through the origin and is parallel to the…

A: Determine a vector equation of the line that passes through the origin and is parallel to the line…

Q: Which of the following vectors is/not perpendicular to the line whose direction vector is (2,-3,5)?…

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Q: Which vector equation below represents the line in R³ that passes through the point (-4, 5, 7) and…

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Q: Let / be the line through the point with coordinates (-2,1,0) in the direction of the vector…

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Q: Is it true that if S is a unital subring of a unital ring, then the identity elements of the two…

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Q: What three points are on the line L: vector r= (2,-5) + s(2,1), sER

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Q: Let / denote the line in R with equation y = = 3x - 2. Let Q = (2, -1). (a) Write the line / in…

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Q: Write the parametric equations of the line through the point (1,2,3) parallel to the vector a =.…

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Q: Let / be the line through the point with coordinates (0,0,1) in the direction of the vector…

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Q: What is the vector equation of the line segment that connects point P(1,−1,2) to point Q (4,1,7)?

A: Given, A line segment passes through the points P1,-1,2 and Q4,1,7 We have, the vector equation of a…

Q: Determine the vector equation of a line that is perpendicular to the line, p = |-4, 4, 9 + t|-1, 3,…

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Q: Let /be the line through the point with coordinates (2,-1,0) in the direction of the vector G) 1…

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Q: A direction vector of the line passing through the points A (3,-1,-2) and B(-1,2,1) is <-4, 3,3). •…

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Vector Arithmetic

Vectors are those objects which have a magnitude along with the direction. In vector arithmetic, we will see how arithmetic operators like addition and multiplication are used on any two vectors. Arithmetic in basic means dealing with numbers. Here, magnitude means the length or the size of an object. The notation used is the arrow over the head of the vector indicating its direction.

Vector Calculus

Vector calculus is an important branch of mathematics and it relates two important branches of mathematics namely vector and calculus.