Use the given pair of vectors, v- 51+6), w -9), to find the following quantities. State whether the result is a vector or a scalar. Enter all vectors in component form (a, b) • v. w Select all the quantities that are vectors.

Q: Show that each pair of vectors is perpendicular.     -4i -3j and 6 i - 8j

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Q: и Match the vectors p, q, r, s, and t with one of the combinations of the u and v vectors from the…

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Q: Use vectors to find the lengths of the diagonals of the parallelogram that has i +j and i- 6j as…

A: Here we have to find the length of the diagonal.

Q: Given the vectors v=3i - 2j+5k and w=-i +4j+2k, find the following: a) 2v-w= b) V•W= ||w|| = c) 12 =…

A: v→=3i-2j+5k and w→=-i+4j+2k

Q: find the component form of the vector. The sum of AB and CD, where A = (1, -1), B = (2, 0), C = (-1,…

A: Given that A = (1, -1), B = (2, 0), C = (-1, 3), and D = (-2, 2)We have to find AB + CD.

Q: For the two vectors a = 7i-4j+2k and b = –6i+3j-5k find the scalar component, comp,b

A: a=7i-4j+2k & b=-6i+3j-5k Now, a·b=7-6+-43+2-5=-42-12-10=-64 & a=72+-42+22=49+16+4=69

Q: Write each of these vectors in a column format: u, v, u + V₁ U - V -1 30° y -1- 60°

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Q: Given the vectors u = and v = , perform the operations below. %3D ü - =

A: We have given two vectors which are given by u→ = 3,7 and v→ = -9,-3. If two vectors  p→ = a,b and…

Q: write the given vector in terms of i and j. u= (-8,5).

A: It is given that, the vector u is, (–8, 5).Assume that, the symbol i represents the horizontal…

Q: Given the vectors u and i = , perform the operations below. %3D -7-0 =

A: Solution after performing operation is given:

Q: express each vector as a product of its length anddirection. 3/5i + 4/5k

A: Here,Given Vector,v=35i+45kWe have to find Product of its length and direction.length of…

Q: Use the given pair of vectors, v= 7i+8j , w= -8j , to find the following quantities. State whether…

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Q: For the vector, find 2 -V, and 4V. V = 2i + 8j Your answ -v =-2i – 4j 4V = = 8i + 32j II

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Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

A: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az

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

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Q: For each pair of vectors, find U V.   . U = -i +j, V =-i - j

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Q: Use the given pair of vectors, v= 5i+6j , w= -9j , to find the following quantities. State whether…

A: Given :-       v = 5i + 6j      w = -9j

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated list…

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

Q: Determine whether the vectors AB and PQ are equal to each other.

A: Solution of the problem as follows

Q: Consider the vectors a= 2i +4j-6k, b*=-31 +k and c = 3j¯- 2k. Find a un vector parallel to - 2a…

A: Given query is to find the indicated unit vector.

Q: Find the area of the parallelogram spanned by the vectors -i+ 2j and i - j.

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Q: What is the area of the parallelogram formed by vectors A = 3ax -ay +2az and B = ax -2ay + 2az * O…

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Q: For each pair of vectors, find U V.   . U =-3i,  V=5j

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Q: Show that each pair of vectors is perpendicular.     2i + j and i - 2j

A: Solution: Consider the given vectors are  a→ = 2i + jandb→ = i - 2j We know that if the dot product…

Q: Use the given pair of vectors, v= -6i+7j , w= -8j , to find the following quantities. State whether…

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Q: Given vectors a, b, c, such that a = 5c + 3d and b = 2c -d, 2a -3b in terms of c and d. express

A: Given vectors, a= 5c+3d b= 2c-d

Q: Draw the vectors in standard position in R2 with their tails at the point (2, -3).

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Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

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Q: Determine the vector 8a – 7b if a = -3i + 2j – 4k and b = 5i + 6j + 2k. 8a – 7b help (vectors)

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Q: in the same sets of axis express the following vectors a=i+j, b=-1+j, c=a+b, d=2a,and e=a-b

A: The vectors are:-

Q: For what values of b are the given vectors orthogonal? (Enter your answers as a comma-separated…

A: To determine the value of b for which the below vectors are orthogonal. −27,b,2, b,b2,b

Q: Solve for the vector x in terms of the vectors a and b. x + 2a - b = 3(x + a) - 2(2a - b)

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Q: Use the given pair of vectors, v= 5i+6j , w= -9j , to find the following quantities. State whether…

A: We apply norm of inner product of addition and multiplication

Q: If A =i-j+3k and B = 2i +6j +3k , Find the vector proj4 and projB

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Q: A plane is flying with an airspeed of 200 mph in the direction of N 50°E and a 40 mi/hr wind is…

A: Let u be the vector representing the speed of the plane and v be the vector representing the speed…

Q: Consider the vectors x1 = (2, 1)T and x2 = (6, 3)T . Determine the length of each vector.

A: Given: x1=2i+j, x2=6i+3j we know that for any given vector v=ai+bj, length l of vector is given by…

Q: 2. Square ABCD is drawn as showWn below with the diagonals intersecting at E. a. State four pairs of…

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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: For the vector, find 1/2(V),−V, and 4V V= (-5,9)

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Q: Write the vector v = (Vị, v½) in terms of the unit vectors i and j.

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

A: Given vectors are 9i-16mj and i+4mj. To find m such that given two vectors are orthogonal. Solution:…

Q: express each vector as a product of its length anddirection. 9i - 2j + 6k

A: The given vector is u=9i-2j+6k. Compute the length as follows. u=92+-22+62=81+4+36=81+40=121=11

Q: In the following diagram, the rectangle ACEG is divided into four congruent rectangles. F E a) List…

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Q: Show that each pair of vectors is perpendicular.     -6i -5j and 10 i -  12 j

A: If two vectors A and B are perpendicular then its dot product A.B=0Dot product:i, j,k are the…

Q: Find the sum of the vectors - î + 23 + k and i = - î + 23 – 2k. %3D j +

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Q: For the two vectors a = 7i-4j+2k and b = -6i+3j-5k find the scalar component, compąb

A: Consider the formula for the scalar component. Find the dot product for a and b and magnitude of a.…

Q: Resolve the vector a = -i+ 4j+9k into orthogonal vectors, one of which is parallel to b =i- 3j – k.

A: Given vectors are a→=−i^+4j^+9k^ and b→=i^−3j^−k^. Here, we using the concept of projection . We can…

Q: ä = 27 + 6j – 4K, b = -3ï – 9j + 6K

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