Consider the vector i 3, and let V 4 = span(ï) C Rº. %3D %3D 5

Q: If v = 2i - 5j and w = i - j, find the vector projection of v onto w.

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Q: Give a vector description of the midpoint M of a line segment AB.

A: According to the vector midpoint formula: Where 'c' is the midpoint position vector of vector 'a'…

Q: Write a vector of magnitude 5, parallel to the plane 3x + 4y + 5z = 10 and perpendicular to the…

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Q: Given Ā =,B = and C =. Find: a) the scalar projection of B onto C – À b) a unit vector ū in the…

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Q: Find a vector v such that v = 15 and v is in the same direction as –li + 13j

A: The solution is given as

Q: If a = i+ 2j +k and b = i+10j + k, find a unit vector with positive first coordinate orthogonal to…

A: The vectors are given as , a→=i^+2j^+k^ and b→=i^+10j^+k^ find a unit vector with positive first…

Q: Find the orthogonal projection of v = i + j + k on b = 2i + 2j,and then find the vector component of…

A: We have given vectors V=i^+j^+k^ and b=2i^+2j^ Vector component V of  along b…

Q: Find the component form of v, where u = 3i - j and w = i + 3j. v = u + 3w Sketch the vector…

A: We have to solve

Q: For the vector v = (2, 1), sketch (a) 2v, (b) −3v, and (c) 1/2 v.

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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: For AABC, let b and c denote the vector AB and AC , respectively. The vector BH is orthogonal to AC.…

A: Orthonormal vectors are perpendicular to each other.

Q: Find c so that the vector v is orthogonal to W = ||

A: Given: v=1c. w=2-1 Vector v and w are orthogonal only if the dot product of vectors is zero.

Q: Show that the vector v = [a, b, c]* is perpendicular to the plane P with equation ax + by + cz + d =…

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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: Let b be a vector in R" satisfying the following equation. 4 3 =Db 7. Then m- and b

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Q: Given a vector A = 3a, - 2a, - 16a, find its components normal to the plane 2x + 2y – z + 8 = 0 and…

A: We have to determine component normal to the plane

Q: Find the vector that makes equal acute angles with the positive coordinate axes and has length 2. O…

A: An acute angle is an angle that measure is less than a right angle (90 degrees). The magnitude of a…

Q: Let b = i + j − k. Find (algebraically) the unit vector in the direction opposite to b.

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Q: For what value of t,if any, is the vector (1, 4t) parallel to the vector (4, - 1)? Not OA. t = -2…

A: If the Vectors u and v are parallel then u=kV , K is any scalar.

Q: Consider the vector v = (−1, 3, 0, 4). Find u such that (a) u has the same direction as v and…

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Q: Consider the vector w = n ^ (v ^ n) where n is a unit vector, and v an arbitrary vector. What are…

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

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

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Q: The vector y which is collinear with the vector u= and satisfies the condition u.v= 3, is O O O…

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Q: 3. Use the given rectangular prism to state a single vector that is equivalent to a) BC + GH A B D E…

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Q: If a = i+ 2j + k and b = i+ 5j +k, find a unit vector with positive first coordinate orthogonal to…

A: Given that     a = i+2j+k and b = i+5j+k We have to find a unit vector with positive first…

Q: What is the subtraction of Vector M from Vector T? M = 5 units T=4 units-

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Q: Given the vector u (6, – 6), find the magnitude - and angle in which the vector points (measured…

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Q: If a = i+5j + k and b = i+ 9j +k, find a unit vector with positive first coordinate orthogonal to…

A: We have to find

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

A: The vector v in direction of u can be found  blew step.

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: Find the magnitude of vector v. Y -2 w X

A: We have to find the magnitude of v

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: If a = i+ 10j + k and b = i+ 11j+ k, find a unit vector with positive first coordinate orthogonal to…

A: Vector cross product of given two vector  is orthogonal to two given vector

Q: Evaluate /1+ x² + y°dS, where S is the helicoid with vector equation S r(u, v) 0 < u < 3, 0 < v <…

A: Given integral ∬S1+x2+y2dS, where S is helicoid with vector equation r^u,v=ucosv,usinv,v We have to…

Q: Given the vector u (2, 2), find the magnitude and - angle in which the vector points (measured…

A: Given that: u→=2,-2. Therefore, magnitude of the vector is= u→=22+-22=22.

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: The vector i +bj-k is perpendicular to the vector I +2j-3k. what is the value of b?.

A: We know that if two vectors are perpendicular to each other then there dot product is zero. Given,…

Q: Find the magnitude and direction of the vector w= (-1,-v3). Select the correct answer below: J Tw] =…

A: To find the magnitude, or length, of a vector, take the square root of the sum of the squares of…

Q: Find a vector w that bisects the smaller of the two angles formed by 15 i + 8 j and 40 i – 9 j. w =

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Q: Given the vector u = ( – 5, – 6), find the magnitude and angle in which the vector points (measured…

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

Q: Find the value of a in the vector i = (a, b) if b = 48 and ||ū|| = 50 %3D v is in Quadrant I

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Q: Evaluate 1+ x² + y*dS, where S is the helicoid with vector equation r(u, v) 0 < u < 2, 0 < v < 2T

A: Given ∬S1+x2+y2dS where S is the helicoid with ru,v=u cos v, usin v, v, 0≤u≤2, 0≤v≤2π. Since ru,v=u…

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: 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: If a = i+ 3j + k and b = i+9j + k, find a unit vector with positive first coordinate orthogonal to…

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Q: Consider the vectors H [0] H . If I is the line defined by the vector w₁, fi W1 = [o] W2

A: Here, in the question three vectors are given:  w1, w2, b  L is the line defined by the vector w1 We…

Q: Let r (t) = |r (t)| = ( the length of the vector is round to one decimal

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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.