B. Find the value of the constant ß such that the vectors: u = ßi + 11j – 3k and 2ßi – Bj – 5k, are orthogonal v =

Q: Find a unit vector that is orthogonal to both u = i − 4j + k and v = 2i + 3j.

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Q: Find the angle 0 between the vectors a = (V3, –1) and b = (0,11).

A: Find angle between given vectors

Q: Find ||7e – 4f|l, assuming that e and f are unit vectors such that ||e + f|| =

A: Suppose e and f be the unit vectors such that e+f=32 First, find the dot product of the vector e…

Q: Decompose v into two vectors, v1 and V2, where v is parallel to w and v2 is orthogonal to w. v=i+j,…

A: A vector parallel to w can be obtained from the following formula, v1=v.ww2w and the other vector…

Q: . Compute the dot product of the given vectors and find the angle between them: a) u = (3,7,-2) and…

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Q: Determine for the three vectors: x = ai+bj+ck, y = 3i+4j and z = di+ej+k %3D %3D %3D where a = 2, b…

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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…

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Q: [:] [] Find c so that the vectors and are parallel.

A: Find c so that the vectors c4 and 25  are parallel. Let u=c4 and v= 25 be two vectors. Two vectors…

Q: (d) Suppose the three vectors x, y, z E R³ are known to be linearly independent. Are the three…

A:

Q: Find the angle between the vector u = i−2j + 2k and (a) v = −3i + 6j + 2k (b) w = 2i + 7j + 6k (c) z…

A: Given That: The vectors, u = i - 2j +2k v = -3i+6j+2k w = 2i+7j+6k z = -3i+6j-6k

Q: Find the angle between the two vectors A = i +j+k and B = 2i+j-k

A:

Q: 3. Find the angles between the vectors: u = 2i + j, v= i + 2j – k а. b. u = 2i – 2j + k, v = 3i + 4k

A: Angle between two vectors, θ=cos-1u→.v→|u→| |v|→ a)  u→.v→=2i+j.i+2j-k       =2+2 u→.v→=4 |u→|=22+12…

Q: Determine m such that the two vectors are orthogonal.

A: Given : 4mi+j and 9m-25j

Q: Find the dot product of the vectors. V = i + 5j; w = -i + j = M.A

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Q: Find b so that the vectors v = i + jand w = i + bj are orthogonal.

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

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

Q: Find the vectors T, N, B at the given point where 0sts 2n. (1 3/3 8' r(t) =

A: We want to find the unit tangent vector , normal vector and Binormal vector

Q: Find the component form of the vector v given ||v|| = 12 following the direction of u (3, –5)

A: Find the component form of the vector v given ||v|| =12 following the direction of u = (3,-5)

Q: Find the dot product of the given vectors. ü =-i +5j v=-6i-2j u. v =

A:

Q: Given the vectors P=3i - j +k, Q =4i +Qy j-2k, and S=2i -2j +2k,determine the value of Qy for which…

A: given the three vectors P=3i-+j+k , Q=4i+Qyj-2k  and S=2i-2j+2k are coplanar vectors. we need to…

Q: Find the cross products U * V and V * U for the vectors U= 3i-j-2k and v=i+3j-2k U*V = ?i +?j+?k…

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Q: Find a vector w perpendicular to both vectors u=2i-j+2k and v=3j-4k w=i+2j-3k w=-2i+8j+6k…

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Q: Let u = a1i + b1 j, v = a2 i + b2 j, w = a3 i + b3 j. Prove the given property by obtaining the…

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Q: Given v = i + 2j, w = 3i + 6j, find projw v. Then decompose v into two vectors, v1 and v2, where v1…

A: v=i+2j, w=3i+6j Now, v·w=i+2j·3i+6j=13+26=15 & w=32+62=45 Therefore,…

Q: Find a set of vectors {u, v} in R“ that spans the solution set of the equations w - х — у — 2z Rw+…

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Q: Consider the vectors y= 3i + 4j + 5k and w= i + j + k. Express the given vector in terms of i, j and…

A: The given vectors v=3i+4j+5k and w=i+j+k

Q: If A is a conutant vector and R= 3xi+ 3yj+ 32K, then grad (3A -R) = ? %3D A O 3A ©9A 27 A

A: A is a constant vector  R=3xi+3yj+3zk 3AR=9Axi+9Ayj+9Azk To find grad(3AR) Let Φ=9Ax+9Ay+9Az gradΦ=i…

Q: How does the cross product i x ì relate to the vectors ở and i geometrically? Use this to compute d…

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Q: Find a set of vectors {u, v} in R* that spans the solution set of the equations w -x-y+ 3z 5w + 2x +…

A: In the question it is asked to write the vector for the given equations. w-x-y-3z=05w+2x+y+3z=0 AS…

Q: If U1 and U2 are orthogonal unit vectors and V = aU1 +b U2, find V.U.

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: Determine the value of the parameter k so that the vectors ū= ki− 2j + 3w, v̄= −i + kj +w are…

A: The given vector are ū= ki− 2j + 3w, v̄= −i + kj +w .

Q: Find a unit vector in the plane of the vectors A = i + 2j and B = j + 2k, perpendicular to the…

A: Consider the given question,

Q: Use the vectors u = a1 i + b1. j, v = a2 i + b2. j, and w = a3 i + b3. j,to prove the given property…

A: Given: u = a1i+b1jv =a2i+b2j w=a3i+b3j

Q: (:) R de u = ve v = ( t2 ) for vectors, show = 2u1v1 + 3u2v2 is an internal product

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Q: (a) Calculate the dot product and angle between two vectors, where u 7j– 2k and v = (1,2,3).

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Q: Which option is equal to the DOT product uV of vectors 3 u = 1 4 -4 26 24 N N

A: The given vectors are: u=314 and v=22-4 Multiply the numbers component wise to find the dot product…

Q: d)) Find the angles between the vectors. .u = 2i + j, v =i+ 2j – k Lu = 2i – 2j + k, v = 3i + 4k u =…

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Q: 3. Find the angles between the vectors: u = 2i + j, v = i + 2j – k а. -

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Q: b) Find out the Vector =y²z?i+x?z?j+z²y²k is irrotational or not?

A: By definition, Any vector is said to be irrotational if the curl of the vector is zero. The given…

Q: Consider the vectors a = 4 i+ 8 j-8k, b = 2 i +k and c = 4 j-5k. Are the vectors a and b+c…

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Q: Find the cross products uxv and vxu for the the vectors u=2i-j-2k and v= i +3j-2k.

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Q: (b) Find the values of s such that vectors -si – 2j+ 5sk and 9si + j+3sk are orthogonal.

A: The given vector are -si-2j+5sk and 9si+j+3sk

Q: Given the vectors v=i+3j w = 4i - j

A: