F(t) = (Cos(Tt), - 1), G(1) = (1, 1, – 1), G'(1) = (2, 3, 2) , Ĝ"(1) = (0, 1, 0) . (F.G) 1) (Gxở) (1) Evaluate Evaluate

Q: find the domain of the vector-valued function.

A: Given: rt=1t+1i+t2j-3tk

Q: Find the magnitude of the vector

A: The given vector is 0,7We know that in a vector a,b the magnitude is a2+b2

Q: What is the difference between a vector and a scalar?

A:

Q: discuss the directional vectors (gradient and curl) with physical examples.

A:

Q: Is the dot product of two vectors a scalar or a vector?

A: We know, Dot product of two vectors gives the product of the length of one vector by the length of…

Q: 2. Find the unit vector in the direction of

A:

Q: Find the angle between the vectors and .

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

Q: Explain what the gradient vector means and what the Euclidean norm of the gradient vector means in…

A: Gradient vector: For a given function f(x,y,z), gradient vector is defined as…

Q: What role does the curl of a vector play in an application?

A: We have to write the curl of a vector play in an application.

Q: Find the orthogonal projection of the vector onto the vector .

A:

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

A: topic- angle between vector and x axis

Q: Describe the result when a point or line is changed by a vector

A: We will describe this.

Q: Let u be a vector of length 3 in the direction of the positive y-axis and let v be a vector of…

A: Vector: - The term vector comes from the Latin word vector, which means "carrier." Vectors transport…

Q: If vector a= and vector b=, find a · b (the dot product of vector a and vector b).

A:

Q: Define the term column vector.

A: Column Vector is defined as a column matrix representing the elements of any vector written in…

Q: Explain how to find the unit vector in the direction of any given vector v.

A: To find the unit vector in the direction of the given vector v, divide the vector v by its…

Q: Use the figure to sketch a graph of the vector. u- V y

A:

Q: Briefly explain why the dot product of a non zero vector with itself does not equal zero whereas the…

A:

Q: Determine the angle that the vector [- /3, – 1] makes with the positive horizontal X - axis

A: To find the angle between the vector -3,-1 and positive x-axis

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.