5. The vector obtained by rotating (0, 1) through an angle of 27/3 radians 6. The unit vector that makes an angle of 1/6 radian with the posi- tive x-axis 7. The vector 2 units long in the direction 4i – j 8. The vector 5 units long in the direction opposite to the direction of (3/5)i + (4/5)j

Q: 1%3D -1 2.

A:

Q: Show that the vector a=(-1,13, – 5)can be written as a linear combination of b = (1, 4, – 2) and c=…

A:

Q: 19. -8 12 -4 2 -3 -1

A:

Q: Using || || and 0, give the vector in (x, y)-form. II

A: We have to write the x,y form of vector v.

Q: Eхample: *-? 3 -", -13 2 2. x, =[4 4 -are Determine if the vectors: linearly dependent or not.…

A: The linear dependency of vectors is solved as follows :

Q: what is the graph of vector B = C - A??

A: First we mark A and C vectors then we find -C vector  The resultant of A and -C will be B as B = A -…

Q: y = -3 7 4 6] 0 Z = 1 -8 15 -7

A: if two vectors are orthogonal, we need to compute their dot product and check if it is equal to…

Q: Define the term Change of basis?

A:

Q: Explain “ some combination gives the zero vector, other than the trivial combination with every…

A: The statement is “ some combination gives the zero vector, other than the trivial combination with…

Q: EXAΜPLE2 Determine whether the vectors vi-(1,-2,3),v2=(5,6,-1),v3-(3,2,1) are linearly independent…

A: Given vectors are v1 = (1, -2, 3), v2 = (5, 6, -1), v3 = (3, 2, 1)

Q: check if the given vectors are linearly independent or not . {(-1, 1, 0), (-1, 0, 1), (1, 1, 1)}.…

A:

Q: (1 point) Express the vector = 8 as a sum of the basis vectors x = and y = %3D -13 xt j. = Netes V

A:

Q: Determine whether each collection of vectors is linearly independent or linearly dependent. Justify…

A: According expert guidelines of Bartleby I have to solve only first three subpart so repost for…

Q: Find the coordinate vector of (-1, 32) relative to the basis {(1, 3), (-1, 4)}.

A: We use the definition of coordinate vector relative to a given basis to answer the given question.

Q: Is every vector in R2 a linear combination of the vectors (1,-2) and (-2,1)? Provide a detailed…

A: Let (a,b) ∈ R2 , We write the (a,b) is the linear combination of the given vector (1,-2) and (-2,1)

Q: 3 [] [] -3 L 6

A:

Q: Define irrotational vector. Is the vector A =(6xy+z³)i+(3x² - 2)j+(3xz² – y)k irrotational? Justify…

A: we have the vector A=(6xy+z3)i+(3x2-z)j+(3xz2-y)k we have to check weather the given vector is…

Q: Find the stable vector of 7 P = 2/7 M5 iii

A:

Q: 13. 1 5 -3 > -2 -9 6 3 h -9

A:

Q: What is the effect of scaling a Vector? Give an example?

A: we need to explain the scaling of vector. and we  need to give an example. First let us define what…

Q: Determine which set of vectors is linearly dependent (a) (b) , (c) (d) (e) (f) O (a) O (b) O (c) O…

A: Recall:A set of vectors is said to be linearly dependent if the determinant is zero.If the…

Q: 17. 3 5 -1 0 0 0 5 4

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: 5 Aaron and Maya want to write the vector u = -5 as a linear comb -19 -2 1 V1 -2 V2 = 1 and V3 = 2…

A: The { v1 ,v2 ,v3 } is not a set of orthogonal vectors.

Q: Is (1, 1) a unit vector? Explain.

A: We know that if any vector a→=a1i+a2j+a3k will be a unit vector then its magnitude a→=a12+a22+a32…

Q: Determine if the vectors vị = (1, –1,3, –1), v2 = (1, –-1, 4, 2), v3 = (1, –1,5, 7) are linearly…

A: We have to determined the vectors v1=(1, -1, 3, -1), v2=(1, -1, 4, 2), v3=(1, -1, 5, 7) are linearly…

Q: Give 2 vectors of length 7 that are parallel to (-1, 2, –2).

A: Find the required vectors

Q: Based on Figure 2 below, explain the process if we want to transform the cow as in figure (with…

A: Assume that the cow is standing on a vector A→. We need to use suitable transformations, to make…