would two independent vectors span a plane whereas two dependent vectors span a line?

Q: The vector that has the same direction as ⟨3,4,3⟩ but has length of 4 is

A:

Q: 'he sum and difference of two vectors à and B are equal in magnitude. Prove lgebraically that the…

A: Given: A→+B→=A→-B→ The magnitude of sum of A →and B→ is , A→+B→=A2+B2+2ABcosθ The magnitude of…

Q: What is meant by the term translation in vectors?

A:

Q: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

A: What does it mean for one vector to be a scalar multiple of another vector? How can you tell whether…

Q: What is a unit vector perpendicular to these two vectors, which are two vectors

A: We have to solve given problem:

Q: How is the angle between two vectors defined and how is it computed?

A: the angle between two vectors is computed using cosθ

Q: If a vector is multiplied by a positive scalar, how is the result re-lated to the original vector?…

A: Explanation:

Q: Find two linearly independent vectors perpendicular to the vector 1 3

A:

Q: Two vectors are considered equivalent (equal) vectors if they and

A: Every vector quantity has dimension as well as mangnitude.

Q: How do you determine if two vectors are orthogonal?

A: If we are given two different vectors , then they are orthogonal if they are  perpendicular to each…

Q: What is the dot product of a vector with the cross product that this vector has with another vector?

A:

Q: The length of the cross product between the vectors k and -k is equal to the zero vector. Select…

A: Given that , the length of the cross product between vectors k and -k is equal to the zero is it…

Q: The sum of the squares of the direction cosines of a vector in space add up to ..............

A:

Q: The cross product of two vectors in R yields a scalar. True False

A:

Q: Show that if u+ v and u - v are orthogonal, then the two vectors must have the same length. What…

A: Hence the two vector u and v have same length.

Q: Finally, verify that the vectors satisfy the Parallelogram Law |||² + ||||? 3. ī = (2, –1), w =…

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: The plane contains the point (2, −1, 6) and is normal to the vector <2, −1, 6>.

A: Given: A plane passes through the point 2, -1, 6 and normal to the vector 2i^-j^+6k^.

Q: It is possible for two nonzero vectors to have a dot product of 0. True False

A: Let u and v be two nonzero vectors

Q: Two linearly independent vectors in R3 span R2, is that true

A:

Q: Draw an example of two opposite vectors that are not parallel or explain why such vectors don't…

A: To find: Two vectors opposite in direction which are not parallel. or, Explain why above two vectors…

Q: Find the dot product of vectors and .

A:

Q: What can you say about the relative position of two nonzero vectors if their dot product is zero?

A: Dot product of two non-zero vectors is zero. We know that two vectors are perpendicular if and only…

Q: What is the magnitude of the cross product of two parallel vectors?

A:

Q: State what the dot product of two non-zero perpendicular vectors is. Justify your response.

A: We have to find the dot product

Q: 9. Explain why four vectors is R³ are always linearly dependent.

A:

Q: Find the magnitude of the horizontal and vertical vector componentsfor a vector.

A: By taking the the vector to be analyzed as the hypotenuse, the horizontal and vertical component can…

Q: If a vector gets multiplied by a positive number, its direction will be .reversed F TO

A: To check: Whether the statement “if a vector gets multiplied a positive number its direction will be…

Q: Express à = (3, 1, –1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

A:

Q: If I was given two-equation of two planes. To find a vector parallel to the plane, do I take the…

A: Suppose the equation of two planes are given. Find out the corresponding normal vectors to the given…

Q: Express à = (3, 1, – 1) as B + Č, where B is parallel to the vector (1, 4, 2) and Č is perpendicular…

A:

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: Compute for the cross product of the following pairs of vectors (-4, 3, 0) and (6, 2, -5). Then,…

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: Two force vectors act on an object and the dot product of the two vectors is 20. If both of the…

A:

Q: why is it not all 4 vectors span W?

A: Lets look at how span of a set is defined :

Q: State the difference between a position veetor and a line vector.

A:

Q: Find the equation of the plane that passes through the point (−2, 8, 4) and contains vectors ⃗a…

A: The equation of plane passing through the point x0, y0, z0 and contins vector a→ amd b→ is n1(x -…

Q: set

A:

Q: 8

A: Given vector is v→=8-7-5 We have been asked to find two linearly independent vectors that are…

Q: How do you find a vector perpendicular to a plane?

A:

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

A:

Q: If a vector is multiplied by a positive scalar, how is the result related to the original vector?…

A: Solution:- If a vector is multiplied by a positive scalar, how is the result related to the original…

Q: How do we know if two nonzero vectors are perpendicular?

A: Two non-zero vectors are perpendicular if their dot product is zero.

Q: when we decompose the vector , what would the vertical component be?

A: Use the decomposing concept of a vector.

Q: The dot product of two vectors is a ________ quantity. For this reason, it is some-times called the…

A: Let A and B be two vectors, the dot product is defined asA.B=ABcosθ, where θ is the angle between…

Q: What are parallel vectors?

A: We have to define parallel vectors. Two vectors are said to be parallel if they have same direction…

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.