What is the volume of the parallelepiped with sides 6i + 9j + 5k, 2j + 5k, and 10k? volume = Find a unit vector orthogonal to the vectors 5i + 9j + 4k and 4i + 9j + 9k with non-negative first coordinate. (Write your solutions using the standard basis vectors i, j, and k. Use symbolic notation and fractions where needed.) unit vector:

Q: Find the of A ABC Where the area vectors AC1,-1,1), B(2,1,1) and are cl-1,1, 2).

A:

Q: find a vector b so that the equation A = b has infinitely many solutions?

A:

Q: Find three mutually orthogonal unit vectors in R° besides +i, ±j, and tk. 3

A:

Q: Find the angle between two vectors: A=31+4j-5k, (1) Scalar product. (2) vector product. B = 3i+4j+5k…

A: To find the angle between two vectors: A→=3i^+4j^-5k^, B→=3i^+4j^+5k^ by using: 1 Scalar product2…

Q: Find the two unit vectors orthogonal to both a = (3, 1, 1) andb = (−1, 2, 1).

A: Given: a=3,1,1 and b=-1,2,1

Q: Find the area of the parallelogram that has the given vectors as adjacent sides. Use a computer…

A:

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

A:

Q: Find the volume of the parallelepiped with sides give by the three vectors a = 2i – 2j+ 3k, b = 5i+…

A: a→ = 2i^ -2j^ +3k^b→ = 5i^ +2j^ +6k^c→ =-3i^ +2j^ -2k^Volume of parallellpiped = a.(bx c¯

Q: Find two unit vectors parallel to v = -2i + 5j – 3k.

A: Given:- v=-2i +5j-3k  To find:- Two units vectors parallel to given vector v

Q: Find projwv. Then decompose v into two vectors, v1 and v2, where v1 is parallel to w and v2 is…

A: v=2i+4j  and  w=-3i+6j. Now, v·w=2i+4j·-3i+6j=2-3+46=-6+24=18 & w=-32+62=45=35 Therefore,…

Q: Use the fact that the volume of a tetrahedron with adjacent edges given by the vectors u, v, and w…

A:

Q: Describe all unit vectors orthogonal to both of the given vectors. −4i + 6j − 2k,   5i + 4j + 9k

A: Concept: The cross product a x b is orthogonal to both the vectors a and ba = −4i + 6j − 2kb = 5i +…

Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

A:

Q: Find the volume of the parallelepiped determined by the vectors ā = (5, 4, – 1), b = (0, 1, 4), č =…

A: Given query is to find the volume of the parallelopiped.

Q: ors a = 6i + 7j + 6k and b = 4i − j + 8k, where i, j, and k are mutuallyperpendicular unit vectors…

A: In this question, the concept of the dot product is applied. Dot Product The product of the…

Q: Find the volume of the parallelepiped determined by the vectors a = (2, 3, – 1), 6 = (0, 2, 1), c=…

A:

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 the volume of the parallelepiped determined by the vectors a, b, and c. a = 31 + 2j - 3k, b =…

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = 1, 2, 4   b = −1,…

A: First find cross product of b and c and take dot product with a

Q: 2. Find two unit vectors orthogonal to both and .

A:

Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

A:

Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Find the volume of the parallelepiped determined by the vectors a =i+3j-k, b= 4i+j-2k and c= - =…

A: a=i+3j-k,  b=4i+j-2k  &  c=-2j+5k

Q: Find the length of the vector. v = (-2, 0, 5, 1) %3D ||| M = %3D

A:

Q: If the triple scalar product of the vectors A = i+ 3j + k, B = 2i -j-k and C= ai + 7j + 3k is zero ,…

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: 6) Use the scalar triple product to verify that the following vectors are coplanar: ü = i + 53 – 2k…

A:

Q: In an Euclidean space E, the vectors u+v and u - v are orthogonal, and the vectors u and u+3v have…

A:

Q: 2. Determine the volume of the parallelepiped formed by the following vectors (a) ā = (2, –6, 2), 5=…

A: To findvolume of parallelpipedmethod:volume of  parallelpiped=a→b→c→a→b→c→=a1a2a3b1b2b3c1c2c3here…

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 2, 3), b = (-1,…

A: Given vectors:                        a=1, 2 , 3, b= -1, 1, 4, c=5, 1, 5

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A:

Q: Find the volume of the parallelepiped defined by the vectors: a= (3, -1, 1), b= (4,0,2) and c=…

A: Given are the vectors  a= (3, -1, 1), b= (4,0,2) and c= (-1,-2,-3) The objective is to find the…

Q: Find the volume of the parallelepiped determined by the following vectors. a) u = (3,2,8), v = (5,…

A: Find your answer below

Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

Q: B. Explain with sketch how can calculate the volume of parallelepiped by three vectors? C. If a =.…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: The vectors 2 and are given by 1= 21+4j-k m and --3i+5k m. Detemine the scalar and vector product à…

A: on solving this we get

Q: Q3/ Show that the vectors (2i + 3j + 6k), (3i – 6j + 2k)and (6i + 2j + 3k) Are mutually…

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1, 3, 3), b = (-1,…

A:

Q: (2) Given the vectors - -- -- --- 1 V1 = V2 = V3 = and w = are there scalars a, b, and c such that…

A:

Q: The angle between the unit vectors a and b is 0. By expanding the scalar product, show that (3a - b)…

A:

Q: Find the volume of the parallelepiped determined by the vectors a, b, and c. a = (1.3,4). b =…

A:

Q: Find the volume of the parallelepiped determined by the vectors a (3, 4, 1), b = (0, 2, 4), = (2, 4,…

A:

Q: Find the area of the parallelogram spanned by the following vectors. u = [4, –6, 5] v = [0, 6, 8]…

A:

Q: Find volume of the parallelepiped determined by the vectors a = (8, 1,0), E b = : (1,4, 1), and c =…

A: The given vectors are a=8,1,0, b=1,4,1 and c=1,1,10

Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

A:

Q: Find the signed volume of the slanted box in R“ generated by the vectors 27 11 11 -2 3 , U2 = V3 =…

A: Form a matrix of the given vectors, A=v1v2v3v4=0-2-1-12-1-236-10-23030 The volume of the slanted box…

Q: Calculate the area of ​​the parallelogram spanned by the vectors and .the⃗ ( 3 ; - 3 ; 1 )a→(3;−3;1)…

A:

Q: If V1 and V2 are vectors defined as V1=3i+3j-3k and V2=2i+j+3k, then: 1- determine the angle between…

A: Given V1=3i+3j-3k and V2=2i+j+3k