Can you find two vectors in R whose dot product is equal to their cross product? No, because the cross product is a scalar, while the dot product is a vector Yes, but only if the two original vectors are identical to one another No, because the dot product is in R while the cross product is in R³ Yes, but at least one of the vectors must be the zero vector

Q: When analyzing the vector To the sum of two vectors, the first is parallel to the vectorA 2i-j+ 3k…

A: I am attaching image so that you understand each and every step.

Q: Find a 2 dimensional unit vector v orthogonal to vector and with another vector w = , hvaing dot…

A:

Q: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

A: According to the formal definition of the term "parallel," two vectors are said to be parallel to…

Q: Find a non-zero vector a perpendicular to the vectors [3] and ū = 2 1

A: Given, v→ = 372  and  u→ = 121   We have to find the non zero x→ vector perpendicular to both the…

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 the cross product of the vectors 214 3k and 6.9- 3k ? Explain why your answer is conne ar…

A:

Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non- %3D orthogonal because the dot…

A:

Q: v, =,v, =, v, =

A: To add or subtract two vectors, add or subtract the corresponding components of each vector. For…

Q: A sum of scalar multiples of two or more vectors (such as c,u + c,v + c,w, where c, are scalars) is…

A:

Q: Find a non-zero vector perpendicular to the vectors and ú =

A:

Q: The vectors a =(1; 4; 2021) and b = (2; -8; 199) are obviously non-orthogonal because the dot…

A:

Q: 11) Use properties of vector to determine the value of the dot product å. b for the vectors ở = 21…

A:

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

A:

Q: The cross product of the vectors a = 2i - j+ 3k and b= 4i – 2j + 6k is likely to be the zero vector…

A: If vectors are parallel then cross product will be zero check they parallel or not

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

A: Solutions

Q: When two vectors are perpendicular, their a. Both are zero b. Dot product is zero c Cross product is…

A:

Q: Define the dot product (scalar product) of two vectors. Which al-gebraic laws are satisfied by dot…

A: Let (a1,a2,a3,....) and (b1,b2,b3,...) are two vectors. Then the dot product is defined by:

Q: Use the definition of the cross product to prove that the cross product of two parallel vectors is…

A: The cross product of two parallel vectors is zero. This can be proved by two definitions of cross…

Q: When decomposing the vector into the sum of two vectors the first is parallel to the other vector…

A:

Q: Find the value of k such that the resultant of three vectors: [1,-1,2], [3,2,1]and [0,1,k] is…

A: Given: [1,-1,2], [3,2,1] and [0,1,k] [2,-4,1]

Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

Q: When decomposing the vector A= 2i - 1 + 3k into the sum of two vectors, the first is parallel to the…

A:

Q: What is the definition of the triple scalar product for vectors u, v, and w in ℝ3?

A: To Define: Scalar Triple Product for vectors u, v and w in ℝ3.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = and v =

A:

Q: The vector a in 3-space of length 3 lying in the yz-plane pointing upward at an angle of 5π/6…

A: let w= aiÌ‚ + bjÌ‚ + ckÌ‚   |w|= a2 + b2 + c2 = 1   W is lying in YZ plane and at an angle of 5π/6…

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

A:

Q: the component of vector a are ax=2.0 units and ay=3.0units while that of another vector b are Bx=…

A: Given components of two vectors: Components of a are: ax=2.0 units and ay=3.0 units, Components of b…

Q: Let x and y be two orthogonal vectors. Then prove that +

A:

Q: a. Without doing any calculation, explain why one might conjecture that two vectors of the form (a,…

A:

Q: Find a vector x = ( c, d) that has dot products x · r = 1 and x · s = 0 with two given vectors r =…

A:

Q: The ________ ________ of two vectors yields a scalar, rather than a vector.

A: Given as  The ________ ________ of two vectors yields a scalar, rather than a vector.

Q: a. Please provide a well explained answer for the follwoing. And explain what are the components of…

A: Components of vector  In two dimensional ,any  vector can divide into two components x -…

Q: We have two vectors: a= a-(:) and b=() What is the resultant of -a plus b?

A:

Q: 1 Find two vectors of norm 1 that are orthogonal to the vectors u = and v = 3

A: Given problem is :

Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: orthogonal to the vectors

A:

Q: True/False: Vectors are completely determined by their magnitude. In contrast, scalars are…

A:

Q: Let p and q be two non-zero vectors. By using the definition of vector product show that pxq =…

A: In the given question, calculate the area of the parallelogram where two sides p and q are given.…

Q: Let the vectors x = (-0.3, –4.6, –3) and y = (4.1, –-2.2, r) Determine the value of r such that the…

A:

Q: uppose ā and b are two non-zero vectors in R3 and they are not parallel to each other. Then, their…

A:

Q: . Let x and y be two orthogonal vectors. Then prove that

A: If x is any vector then Euclidean norm or 2-norm is denoted by ||x||2 and is given by  ||x||2 =…

Q: True or False Of all of the possible scalar multiples of a vector v, the orthogonal projection of u…

A: This is a result which states that " Orthogonal projection of any vector a onto b is closest to a"

Q: Show with the help of the calculation rules for the scalar product for vectors ||x – 2 y|| = ||x||2…

A: The property used here are b2=b·b x·y=y·x cx·y=cx·y=x·cy Consider the left hand side of the given…

Q: Find a non-zero vector perpendicular to the vectors -2 and ü = 2 ||

A:

Q: Use a dot product to determine whether the vectors u = ⟨1, 2, 3⟩ and v = ⟨4, 1, -2⟩ are orthogonal.

A:

Q: In a three-dimensional space we have a vector R =( 4at + 3aj+ 5ak). Another vector S has the same Y…

A: 1st we will find other two vector R →  and T→ and then will use dot product and cross product to…

Q: In Cartesian coordinates, a rank-2 tensor is given by Į = Tr£xx + Tvz£xz+ Tyy£yy and a Cartesian…

A:

Q: find two vectors such that ^2 = ||x||^2 * ||y||^2 where * stands for the euclidean norm

A:

Q: Find the two unit vectors orthogonal to both a = (4, 1, 1) and b = (-1, 4, 1). %3D

A: