(a)Show that the vectors a = 2i + 4j8k, b = 3i -j + 3k and c = -5i + 11j - 25k are coplanar.

Q: Find two vectors of norm 1 that are orthogonal to the vectors u = (2,−3,4) and v = (3,1,−5)

A: The cross product of two vectors is perpenducular to both of the vectors. The cross product of the…

Q: If three vectors vị, v2, V3 E R° are linearly dependent, then one of them must be a scalar multiple…

A: GIVEN THREE VECTORS v1, v2, v3 belongs to R^3 are linearly dependent

Q: The projection of the vector 5î + 5ĵ – 5k onto the vector –4î + 2ĵ – 4k. | |

A: We have to find out

Q: Calculate r'(t) and T(t) and evaluate T(1). r(t) = (6 + 7t,12,5 – 1²) (Give your answers using…

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Q: The normal vector to the vectors u = (2, 1, 1) and v = (1, -1, 3) is:    4i - 5j + 3k  4i - 5j -…

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Q: Find the vector projection of v = -6i + 10j – konto w = = 2i + j − k (Give your answer using…

A: The given two vectors are  v=-6i+10j-k  and w=2i+j-k

Q: The unit vector of the column on the plane 2x + 2z - 4y = 3 is the vector.

A: THE GIVEN QUESTION CAN SOLVED AS SHOWN IN STEP2.

Q: Suppose two vectors F and ü: r=3i+25-4k v = 2i - 1ĵ+3k where i, j, k are the unit vectors in the…

A: Since you have posted a question with multiple subparts, we will solve only the first three subparts…

Q: Find all the vectors of the family (2-jx, j4, 2-j5, jx) that are of hermitian length equal to 21.

A: Let Y=2-jx,j4,2-j5,jx Length =Y=4+x2+42+4+25+x2   Y=49+2x2 49+2x2=2149+2x2=2122x2=392x=±14

Q: Let a = (6, −3, −5) and b = (7, -2, 10) be vectors. (A) Find the scalar projection of b onto a.…

A: Let  be vectors.(A) To find the scalar projection of .(B) To decompose the vector  into a component…

Q: Find a vector orthogonal to both v and u. V = 2i - 2j + k, u = -4i - 4j + 5k -6i - 7j + 7k 6i + 7j +…

A: Given is           v = 2i -2j +k           u = -4i-4j +5k         two vector a & b said to be…

Q: Find the equations of the traces in the coordinate planes and sketch them z = x2 +9y2

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Q: Let a = 2i – j - 3k and b = 3i – j-k %3D (a) C ) Find two unit vectors orthogonal to both a – i and…

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Q: Is the pair of vectors 2i – j and -i+jperpendicular? no yes

A: Given vectors 2i-j and -i+j Two vectors are perpendicular if and only if dot product of those two…

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: Determine whether or not the 3 vectors of P2(R), p1(t) = 1−t², p2(t) = t, p3(t) = −1+t+t² arly…

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Q: Apply Gram-Schmidt orthogonalization to the column vectors of A, a1 = (1, 1, 0)T ,a2 = (1, 0, 1)T ;…

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

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Q: Show that the vectors a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k are linearly independent. Find…

A: The given vectors are  a = 3i−j+4k, b = i−3j−2k and c = 4i−3j+2k

Q: Compute the first two steps of the Jacobi

A: Given,          2-10-12-10-12uvw=020

Q: Find the projection of vector u⃗ = −i + 5j + 3k onto the vector v = −i + j − 3k?

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

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Q: O Find a vector perpendicular to both i- 3j+2k and 5i-j-4k

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