W 2-Find a vector that is perpendicular to both B = i +j-k B = 4i – j 1. A = 2i +7j – 4k | > 2. A =-i -2j +4k

Q: H.W: vectors u =-2i + 4 j – v5k and v = 2i – 4 j + /5k , find: 1. the vector proj,u 2. the scalar…

A: Given  u=-2i+4j-5k & v=2i-4j+5k

Q: Q. (a) Find the vector projection of v onto w. (b) Decompose v into two vectors vi and v2, where vi…

A: Given v=2i-3j+k,w=i-j+kAim: To find vector projection of v onto w.We know that vector projection of…

Q: Q3): If A = 2i-j+ k, B = i + 2j - k and C = i + j - 2k, find unit vector orthogonal to A in plane of…

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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: If the vector K ag+Lay+ Ma, shows the maximum increase rate and direction of the scalar Vat point…

A: If the vector Ka^x+La^y+Ma^z shows the maximum increase rate and direction of the scalar V at point…

Q: Find a vector parametrization of the line through P = (3, –8, 5) in the direction v = (-2, 0, 3)…

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Q: 3. Express the following vectors in Cartesian (component) form. Z a) f has magnitude 20 and…

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Q: 35. The position vectors of the points A and B are OA =2i + j- 4k,OB =-2i +4 j – 2k , a vector…

A:

Q: Q3: A given vectors r, = 2i - j+k, r=i+3j-2k, r, =-2i +j-3k and r=3i+2j+5k find scalars a, b and c…

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Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i - 3j-k, find vector normal to A and In plane of A and, B. N

A:

Q: 47. T'he points A and B have position vectors (i - j+ k) m and (2i – 3j + 4k) m respectively. The…

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Q: 4. Find two unit vectors orthogonal to both j-k and i+j.

A:

Q: 5) Find the unit vector in the direction of v = 2i + j+k 1 - i+-j+ d) i+j+k 1 1 j+ V5 а) V5 k b)

A: We can solve this as follows:

Q: 3. The line through the point (2, 2.4, 3.5) and parallel to the vector 3i+ j – k Answer + (2i+ 2.4j…

A:

Q: 13. Consider the position vector i = (1,0, 0) in R³. Describe the set of position vectors v in R³…

A: Given, i=1,0,0∈ℝ3

Q: A particle is moving along the curve having the vector equation R(t) = ti+t²j+ tk. Find the vectors…

A: The given position vector is  Rt=t i + t2 j + t k.   The velocity vector is given by Vt=R't=i+2t j…

Q: 27-j+4k sī +2j-2k.

A:

Q: (b) y =u°+In(2u), where u = e 4. Consider the vectors u,v and w are defined as u = -i+2j+2k, v =…

A: 4. Given the vectors u , v , w.

Q: Q1A)The vectors A = 3i+j+ 4k, B = 2i3j-k, find vector normal to A and In plane of A and, B.…

A: Since you have posted multiple questions. As per guidelines we"ll solve only first first question.…

Q: A vector orthogonal to both u = 2i + j – 2k and v = -j+k is اخترأحد الخيارات -i – 2j + 4k .A | i –…

A:

Q: Let i = 47 – 11 and y = 4j – 10k be two vectors. Find the value of the scalar product x · y.

A: See the detailed solution below.

Q: Q2] (A) Find the surface area of the portion of the half ball with radius a which cuts off by the…

A:

Q: Let x = p+ su +tv be the vector equation of a plane in R³. Then the plane passes through the origin…

A: Vector equation of a plane:

Q: 2. Let Ā and B be nonzero vectors. Find k e R such that B – kĀ is orthogonal to Ā – B.

A:

Q: The projection of the vector ( i-j+5) onto the vector 2 i+ j + 4 k is

A:

Q: Q3. Prove that (only one): a- G = ax-ay is a unit vector? %3D b- L = 6a, – 3a, + 2a, and M = 3a, +…

A:

Q: - The vector component of the force (3i- j + 2k)N in the direction of the vector (-4j + 3k) is A…

A: The solution is given as

Q: For the vector function G(t) = -3cos(2t) i+3sin(2t) j+k, find: dG (b) dt dG (c) G• dt dG dG (d) Gx…

A:

Q: 1. Given the 3-dimensional vectors: A = (xy)i + (2yz)j +(3xz)k B = (yz)i + (2xz)j +(3xy)k Determine…

A: Given; A=(xy)i+(2yz)j+(3xz)k   B=(yz)i+(2xz)j+(3xy)k.

Q: 2:/ If the vector u=-8i-2j- 4k & v 2i + 2j + k, find: a) v.u, vl, lu| b) vxu c) The cosine of the…

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Q: 1 (b) Find the span of vectors i = |0 and j = |1 in R3

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Q: (B3) let V1, V2, . , Vn vectors in R". For all 1si, jsn, suppose that 1, si i= j, %3D 0, si i+ j,…

A: Let V(F) be a vector space. Let S=u1,u2,.........,un be a non empty subset of V. Then, the set is…

Q: ind the component form of v, where u = 4i - j and w = i+ 4j. V = u + 4w ši + 3j ketch the vector…

A: We asked to find the vector component

Q: H.W 3- Find a vector V =xi +yj +k that is orthogonal to both A = 3i + j +k _and B = 3i +2j +2k .

A:

Q: Find the domain of the vector function r(t) = (sqrt(25-t^2),e^(-2t),ln(t+3)

A: Given:        r(t)=⟨25−t2,e−2t,ln(t+3)⟩

Q: 1 3 8. For r = , y = |, compute the following: -1 -2 a) I y b) ||r|| c) a unit vector vector in the…

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Q: Q8. Find the equation of the plane passes through the point (1,2,3), parallel to the vector…

A: We have to find the equation of a plane passing through a given point and parallel to two vector.…

Q: Q/ B/ If vector A = 3i – 2j + 7k and B = -i+j- 3k , find the area of triangular between vector A and…

A:

Q: Find a vector function that satisfies the conditions r"(t) = 12ti – 31-/2j+2k, r'(1) = j, r(1) = 2i…

A: We have to find a vector function that satisfies the conditions…

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

A:

Q: 10. In the diagram, M is the mid-point of CD, BP:PM = 2:1, AB AD = z. = x, and AC = y and %3D…

A: Given that:                               NOTE: As per our answering guidelines, we can only answer…

Q: If a = i+ 8j + k and b = i+ 13j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: 3. Find two unit vectors orthogonal to both j − k and i + j

A: We will find the two unit vectors orthogonal to j-k and I+j as following.

Q: 10. Let the vector v = 2i -3j + k, and the vector w = = -i+3j+ 2k. Find v x w.

A:

Q: Given the vector function 7 (t) = (3t, 5t", – 3t° + 2) - Find the velocity and acceleration vectors…

A: Given that vector function r→ t=3t,5t2,-3t5+2 To find the velocity and acceleration at t=-1Solution…

Q: (b) Oppositely directed to 6i – 4j + 2k. 6 i v = V56 2 k + V56 V56 (c) Same direction as the vector…

A: Given problem:- Find unit vectors that satisfy the stated conditions. (b) Oppositely directed to 6i-…

Q: 98 25) Gvon vectors v= 30tj and w=-2i -j. Decompose v into two vectors V, and Vz, where V, is…

A:

Q: Q3) Find the vector ž, which is perpendicular to vectors ã = (2,3, –1) and b = (1,–2,3) and…

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Q: If a = i+ 4j + k and b = i + 8j + k, find a unit vector with positive first coordinate orthogonal to…

A: Given : a=i+4j+k and b=i+8j+k.