Sketch the vectors ro =< -1,2 > and v=< 1,1 > and then sketch the six vectors ro±v,ro ± 2v,ro± 3v. Draw the line L: –1+ t, y = 2 + t, and describe the relationship between L and the vectors you have sketched. What is the vector equation of L?

Q: a= b=

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Q: Specify the unit vectors a = 2i + 3j-k and b = 3i + 4j.

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Q: A vector has initial point (−11,−12) and terminal point (20,−19) The component form of the vector…

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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: Find the angle between the vectors u = (-3,1,–2) and v = (-7,-5, 2) %3D

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Q: What is a derivative table?

A: This is the application of calculus.

Q: Find a unit vector parallel to the line y = 7x – 3. Use the scalar product to find the angle between…

A: The equation of given line is:.Suppose,.So,.So, the parametric equation of the line is:So, the line…

Q: 3. (7-9) A vector has an initial point at (1, –1) and an endpoint at (8, 6). Write the vector in…

A: The given start and endpoints of vector are (1,-1) and (8,6) We know that the magnitude of a vector…

Q: = (2, -1) and v= (-2,3). Sketch u and v. Then sketch (show how the vectors are adding up) and…

A: Given, u=2,-1,v=-2,3

Q: Find the angle between the vectors and .

A: Given vectors a=-2i-j+3k b=2i+j-3k

Q: Find the angle between vector [2, −5,7] and the x-axi

A: topic- angle between vector and x axis

Q: A vector with initial point at the origin and the terminal point on a unit circle can be written in…

A: Let A and B are the initial and terminal point if a vector then the representation of the…

Q: let u = [-3, 4] and v = [2, -5]. Find (a) thecomponent form of the vector and (b) its magnitude. 5v

A: Given that u=-3, 4  and  v=2, -5. This implies that, 5v=5·2, -5=5·2, 5·-5=10, -25 Thus, the…

Q: Let u = (-3,4) and v = (2, –5). Find (a) the component form of the vector 3u – 4v and (b) its…

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Q: Express the vector v with initial point P and terminal po P(-9, -7), Q(-3, -3)

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Q: TRUE or FALSE: Vectors u = (-4, 1, -2) and = 1 7 1 1

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Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: Find a unit vector u in the direction opposite of (-1,-9, –7). | u =

A: First we find the vector of the same magnitude in the opposite direction of the given vector and…

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.