u=2i+4j+k   v=-i +3j+2k   w=i +5j-3k find u•v and v times w  also find the volume of the parallelepiped bounded by the three vectors

Q: Use the new command from Example 3 above to find the volume of the parallelepiped formed by vectors…

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Q: Suppose that A, B, and C are the corner points of the thin triangular plate of constant density…

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Q: Find a vector B such that F = V × B and V · B = 0 where F %3D (x + Зу, у — 2z, х - 2z). %3D

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Q: 3 Among all unit vectors u = y in R', find the one for which the sum x + 8y+ 4z is minimal.

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Q: 11. Find the volume of the parallelepiped determined by the vectors u = 2i + 3j - k, i + j - 2k ,…

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Q: c) Find all value(s) of t such that the vectors 2t i – 2 j-k and 2t i+ 3t j – 2 k are perpendicular.

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Q: Find the volume of the tetrahedron spanned by the vectors u = 13 (4,0, 8), v = (0,2, 3), and w = (0,…

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Q: Hiw.2 Censider the PakullelePifed with šider: A=3i+2j+k Bziti+zkyczi+sj+3k;. thens t-Find the…

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Q: 3. (.J 6) For two vectors u = [1,0,0]" and v = [1,1, 1]", find a third vector with unit length such…

A: Given: Lt us consider the given, u→=1,0,0v→=1,1,1

Q: 3. (а) Consider the vectors ū = i – 6j + 4k, ở = 2i – 5j – 3k and w = 6i – 2j + 3k Show that ū x (T…

A: Use the formula for determining the cross product of two vectors  Substitute the values given and…

Q: (a) Find a vector n perpendicular to the plane z = 8x + 9y. n = (b) Find a vector v parallel to the…

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Q: The vectors (i + j) , (i – j) and (k – i) are Parallel to each other A. Perpendicular to each other…

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Q: Show that (u, v) = (8u + 3, u – v, 15u + v) parametrizes the plane 2x – y – z = 6. Then: (a)…

A: For part (c):  According to the given information it is required to express the function

Q: c)) find a unit vector perpendicular to plane POR. P(1, -1, 2), Q(2, 0, – 1), R(0, 2, 1) . P(1, 1,…

A: We have to find the unit vector perpendicular to the plane according to the given information

Q: I need help for problem 9. Thanks!

A: For (a)

Q: Use a scalar triple product to find the volume of the parallelepiped that has u, v, and w as…

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Q: Q#1 Evaluate ſ,A.n ds , where A = z i+ xj-3y°z k ( i, j, k are unit vectors) and S is the surface of…

A: Let ∅=x2+y2-16  Then the normal to the surface S is ∇∅=2xi+2yj The unit normal is…

Q: i. Find b × c in terms of λ . ii. Show that a · (b × c) is independent of λ .  iii. Find the…

A: i)

Q: where r is the position vector 6. Show that A) - da = | (Ax (Vf)) · da + fA- dl 7. Evaluate the…

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Q: 29. Find the volume of the parallelepiped PQRS if the vectors V(PQ). V(PR), and V(PS) are,…

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Q: A- Find the value of the constant (a) such that the volume of the paralleiepiped determined by a-…

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Q: Write the equation of the plane with normal vector n=5jn=5j passing through the point…

A: Given,

Q: (A) Aunit vector u in the direction of the vector P( 2,0, 2) to Q( 4,2,0) (B) The vector projection…

A: To Find: (A) a unit vector u               (B) Vector projection of u on to v              (C)…

Q: Show that (u, v) = (8u + 3, u – v, 15u + v) parametrizes the plane 2x – y – z = 6. Then: (a)…

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Q: Find the volume of the parallelepiped spanned by the vectors i +j+ k, i –j+k and 3k.

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Q: verify that (u * v) . w = (v * w) . u =(w * u) . v and find the volume of the parallelepiped (box)…

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Q: H.W 6- Find the volume of the parallelepiped for which the given vectors are three edges. C= 2i +2j…

A: Volume of parallelepiped having a1, a2, a3, b1, b2, b3, c1, c2, c3 vectors as edges is given by…

Q: H.WO Use Gramer Rule to Find ,z -2X + 3y-Z 1 X + 2y-2-4 -2x -j+Z = -3 Hwの Find the area of A ABC…

A: Part A:  The three equations given are, -2x+3y-1z=1 --(1) 1x+2y-1z=4 --(2) -2x-1y+1z=-3 --(3)   Part…

Q: Find a set of vectors S that spans the vector space V. Begin by parameterizing V; show your work. I.…

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Q: 4. Let u o, where o is the zero vector. Show that there are exactly two unit vectors that is…

A: This is a problem of vector algebra.

Q: Consider the parallelepiped with adjacent edges u = 7i + 4j + k v = i+j+9k w =i+8j + 8k Find the…

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Q: 43. Volume of a Parallelepiped Find the volume of the parallel- epiped determined by the vectors u =…

A: Rewrite the given vectors. u=2i−j=2i−j+0kv=2j+k=0i+2j+kw=3i+j−k

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. N, = 2î…

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Q: Calculate the work done by the force F= y^3(y over 3).i + x^3(x over3).j  along the displacement…

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Q: a nonzero vector parallel to the line of intersection of the two planes x + 3y + 5z = -3 and x + 3y…

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Q: Two sphere of radii r1 and r2 cut Orthogonally prove that the radius of common circle is (r1r2)…

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Q: (2t, 1 – t, 4t) is a parametrization of the line passing through the point (0, 1,0) and also…

A: The statement : <2t, 1-t, 4t> is a parametrization of the line passing through the point (0,…

Q: (a) Find a vector n perpendicular to the plane z = 8x + 9y. (b) Find a vector v parallel to the…

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Q: The vectors (i + j) , (i – j) and (k – i) are Parallel to each other A. Perpendicular to each other…

A: The given vector are perpendicular each other.

Q: Q5.Find a vector parallel to the line of the intersection of the planes 2x + y – 2z = 5 and. %3D N =…

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Q: Find x if the vectors a =i+j+ 2k;b = xi-j+k; coplanar or linearly dependent.

A: Given,       a=i+j+2kb=xi-j+kc=3i-2j-k

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

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Q: \lfu = i + j-k, v = 2i+j+ k, w = -i - 2j + 3k, find 1) The area of the parallelogram determined by…

A: Given u→=i+j-k,    v→=2i+j+k,   w→=-i-2j+3k   To Find: 1) The area of the parallelogram determined…

Q: Vhich of the following is the volume of the parallelepiped determined by the vectors u=i+j-k,…

A: volume of parallelepiped V =( u * v ).w

Q: 2. 3. 3. t.5-2 show that O vector Cusis Perpendicular to the vectors LU) und LW) 2 vector Cs…

A: Two vectors a→ and b→ are said to be perpendicular if their dot product that is a→·b→ is equal to 0.…

Q: Exercice 1 Given the vectors u ( 1;2;3) and v(-1;–1;2). Determine the vector w ( 7; y;z ) orthogonal…

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Q: Find the distance between u and v. (0, 2, 1), v = (4, -1, 1) = n d(u, v) = %3D

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Q: 5 . For vectors a and b in R² prove Lagrange's identity: ||a x b||? = ||a||*||b|l² – (a - b)? 6.…

A: Use cross and dot product of vector

Q: Find the angle between the two given planes: f = x+y+z-1, and f, =x-2y+3z-1. hint: Find the normal…

A: The angle between two planes can be easily found if we know the normal vectors to the planes.