9. What is the component form of the vector that translates the top triangle to the bottom triangle? 4. 2. 6. -2 -2 -4 -4

Q: How to calculate the cross products of vectors ? = {3,4,7} and ? = {4,9,2}?

A: GIVEN: Two vectors {3, 4, 7} and {4, 9, 2}

Q: 28 74.6

A:

Q: 4. Write the vector equation for a line parallel to the line L: F = (1,-7)+t(2, -3), t € R…

A: Introduction: In three-dimensional geometry, a line can also be described through a vector equation,…

Q: What is the component form of the vector with an initial point of (-2, 5) and a terminal point of…

A:

Q: If the vectors a=(2,5,-1) and b3(3,-3,k) are orthogonal, the the value of k is

A: Given : a = 2,5,-1b = 3,-3,k

Q: 3. Determine the vector equation for the line with symmetric equations*=3+22=1

A: Given: Symmetric equation of line: x-34=y+25=z-13 To find: Vector equation of line.

Q: 9. Illustrate how you would find the unit vector having the same direction as vector (p.q.r).

A: Formula: The unit vector in the same direction of a vector v→ is given by, v^=v→v Given: p, q, r To…

Q: How many vectors can represent a line given by vector (-3,-5, 1) + (7,2,3)

A: The Equation of the line passing through a point A a→ and vector v→ P = Position vector

Q: 4. If d and bare unit vectors and |a + 61= v3, determine (2d – 38)- (+2). %3D

A:

Q: How do you find the cross product a x b of two vectors if you know their lengths and the angle…

A: If you know the length of the two vectors a and b then, you essentially know |a| and |b| And then…

Q: 1. Use the right hand rule to determine which of the following vectors ( î, -î, ĵ, -ĵ, k, –k ) would…

A: According to Bartleby guidelines, we are supposed to do only one question. If you want more to be…

Q: The area of a parallelopiped that is formed by two vectors A and B can be obtained mathematically…

A: It's area of parallelopiped is given by A×B.

Q: What is the component form of the vector represented by 8a when a = (-5, 3)? Enter the answer in the…

A: Scale product of the vector

Q: 6 2 Show that it is vectors are lineas dependent line or independent.

A:

Q: c) Is the point (4,3, 3) on the line (L1) ? Why or why not ? d) Determine the vector equation of the…

A:

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

A:

Q: How many different direction vectors does a line have?

A: Query - How many different direction vectors does a line have? Answer- Direction numbers is a number…

Q: Suppose L(5, 4) was reflected across the line y = x then translated along the vector . What is the…

A:

Q: 03, If a=(3,-1,1), for what value ofe is the vector b-(3,c,-1) perpendicular to a?

A:

Q: 2. Find the cross products of the vectors in the diagram above.

A: The concepts to be used: (i) The components of vectors can be written in terms of cosine and sine.…

Q: u = (- 4, -1,1) and v = (8, -4,3), a unit vector in the direction of the vector w = 3u-v corresponds…

A:

Q: If the magnitude and direction of vector ? are 2√5and 153.3°, what are the components of vector ??

A: Simplification of vector

Q: 2b.) Suppose u, w are two vectors in R' satısfyıng uXu = 4, wXw uxw = 8. What is the distance…

A: Given u and v be two vectors in ℝ7 satisfying u×u=4, w×w=16, u×w=8

Q: 6. Find the unit vector in the same direction as v. If u = (-12,8) and v = (-5,-12), find:

A: Consider the vectors u=<-12, 8>,    and    v=<-5, -12>. Need to find the unit vector in…

Q: Which of the vectors OP = (1,-1,5) and og = (2,-1,0) is not perpendicular to the line Li- - z.…

A: The equation of a line that passes through the point x0 , y0 , z0 in three dimensional space is…

Q: The volume of the parallel pipe formed by three vectors A, B, and C is 50 cubic units. if A(-2,6,3),…

A:

Q: 2. The unit vector in the same direction as (-6, 12) is

A:

Q: How can you tell when vectors span a certain R^? Please explain in the most simplistic detail>

A: Let S=v1,v2,v3 And v1=1-12;v2=213;v3=-102 Does SpanS=ℝ3? if any vector in ℝ3 can be expressed or…

Q: write the given vector in terms of I and J. u={-8, 10} u=???

A:

Q: Q1) If a vector gets multiplied by a positive number, its direction * .will be reversed

A: Given statement : If the vector gets multiplied by a positive number, it's direction will be…

Q: The vectors (8, 6) and (k, 12) are parallel. What is the value of k

A:

Q: 13. Describe the vector that translates LMN to L'M'N’. 6. L' L 2 N' M -6 -4 -2 4 6 N2 M -4 -6 4,

A: Translation vector

Q: B: Find area of triangle whose vectors P1(4,2,0), P2(-1,1,1), P3(0,4,3) (

A:

Q: - ()--)- 1 Let a = 2 and b = be two vectors. What is Jal2|b|2 - |a · bl2 ?

A: Here,  Given that  two vectors  . So, we find the value of  |a|^2.|b|^ - |a.b|^2

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 3. +-b and Aa…

A: We have to find the value of lambda by using the data given above

Q: 1. If a and b are two non-parallel vectors and the position vectors of P, Q and R are 1 3, a +2b,…

A: The equation of the line PQ is : PQ=Q-P=12a+34b-(a+2b)=12a+34b-a-2b=-12a-54b The equation of the…

Q: Write down the line equation a) given a point Q and a vector v. b) given two points R and Q.

A: Since, our aim is to find the equation of a line that is :-(a) passing through a given point Q and a…

Q: 6. Write as a linear combination of the vectors

A: solving by linear combination of the given three vectors by converting into syatem of equation...

Q: -6 --5 Let z = and y . Find the vectors v = 47, ủ =i + ÿ, and w = 47 + y. w = || ||

A:

Q: Since A, B and C vectors are perpendicular to each other, A, B, C, =? A -6) â, 1 (8) â, + A‚⸠B 19)…

A:

Q: 4 3 Which weights should be used for b = a, vị + a2 V2 to obtain the vector b = ? 2 a1 = Ex: 42 az =

A: Solve the following

Q: 2. Find a vector that has the same direction as (-3, 5, v2), but has length 8. 3. If ā = 21 – 43+ 4k…

A: We'll answer one question since the exact one wasn't specified. Please submit a new question…

Q: If u = (1,-3,2) and v = (-2,3,4). Find the distance between the vectors d(u, v) and d(v, u).

A:

Q: What is the angle in degrees between the two vectors (2, 4. -1) and (4, 8, -2)? Note that the…

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Q: 10. Calculate the area of the parallelogram formed by the vectors a =(3, 2,-2) and b = (2,-1,2).

A:

Q: a) tor which values on a are the vectors 87 2 -- a linearln independent?

A:

Q: (5)  Please explain in words how a student would determine the normal vector to the direction vector…

A: explanation of determination of normal vector are as follows

Linear Algebra

In mathematics, problems can be solved by the arithmetic operators like addition, subtraction, multiplication, and division. In algebra, we represent the numbers by any letter called a variable. If these variables are of degree 1, then it is studied under linear algebra. The first-degree equations involving algebraic expressions are called linear equations. That is, if you represent it by drawing a graph you will get a straight line.