Given vectors A 2a, + 4a, + 10a, and B = -5a, + a, – 3a, find %3D (a) A + B at P(0, 2, -5) (b) The angle between A and B at P (c) The scalar component of A along B at P

Q: The following diagram shows the parallelogram ABCD. B A D Let AB =p and AC=q. Find each of the…

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Q: For what values of b are the vectors and orthogonal?

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Q: The points P and Q have position vectors a + b and 3a – 2b respectively relative to the origin O.…

A: vectors

Q: For what values of h the vectors -3.72%3D linearly independent are

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Q: For what value of t, if any, is the vector (8t, 2) parallel to the vector (4, -1) ?

A: Given vectors:A= <8t, 2> and  B= <4, -1>

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: If a = 2i -j+2k and b =i+2j-2k, find two vectors c and d satisfying all the following conditions:…

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Q: Given vectors ū = [3,2, –1] and v = [-2,2,4] , calculate the following: %3D %3D a) 2ū + 30 b) ū · v…

A: Use vector properties.

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: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C = ix - iy + iz Find the following:…

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Q: In a triangle ABC, points E and F are on the sides AC and BC respectively, such that AE is 1/3 of AC…

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Q: The vectors a, b and c are such that 2a – b+c= 0. If a = 4i – j+k and b = i- 2k , find a unit vector…

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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: For the given vectors a and b, find the cross product a x b. a = i +j+ k, b = 5i - 2k

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Q: Given the vectors u=(5,8) and w =(-4a,5a+5), where a is a constant. If it is known that u' +w°…

A: u→=5,8w→=(-4a,5a+5)

Q: Given two vectors e1=(1, 0, 0)T and e3=(0, 0, 1)T in the 3D space, figure out b) e1-e3

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Q: Given the vectors a=(-1,5,-4) and b=(2,-7,2) find the vectors x € R3 , with magnitude v371 and…

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Q: For the given vectors a and b, find the cross product a x b. a = 6i – j, b = -6j + k %3D %3D a x b =

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Q: 2. Consider the two vectors a and b, as graphed below. 2a Plot the result of a +b on the same axes.…

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Q: 1. Assume the lengths of the vectors 2a – b anda+ 3b , assuming a = (2,1,3) and b = (-1,2,2)

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

Q: Find (a) the dot product of the two vectors and (b) the angle between the two vectors.

A: The vectors 4i^-j^, -3i^+2j^

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: Consider the points A=(1,2,3), B=(-2,1,0), and C=(0,3,1). Adding the vectors, find 2AB+3AC.

A: To find 2AB +3 AC

Q: The points P and Q have position vectors a + b and 3a – 2b respectively relative to the origin O.…

A: Given OP→=a+b, OQ→=3a-2b

Q: In the rectangular prism shown below, OA=a, OC=b and oD =c. Express each of the following vectors in…

A: We have to express sides of rectangular I  prism in terms of vector a, b, and c

Q: In the rectangular prism shown below, OA=a, OC =b and oD =c. Express each of the following vectors…

A: We have to write following side of cube in vector form on the basis of given vector.

Q: Find the angles between these vectors, giving your answer in degrees to one decimal place. ) -3 and…

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Q: A = x6- y9+z3 B = x6- y3+z9 C = x 2- yl-zl For the given vectors A,B, and C show that whether C is…

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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: Given the vector component of D(2, – 6, - 5) and G(1,2,3), find the vector of D that is parallel to…

A: Given vectors D(2, -6, -5) and G(1, 2, 3) We need to find the vector of D that is parallel to G

Q: 2 Given the three vectors A = 2i +j, B = i+ k, and C = 4j, find the following (a) A. (B + C) and (A…

A: Given vectors: A=2i+j+0kB=i+0j+kC=0i+4j+0k

Q: Given the three vectors A = 3ix + 2iy – İz B = 3ix - 4iy – 5iz C= ix - İy + İz Find the following:…

A: We have to find the vector

Q: 10î - 4ĵ +7 k̂ and B =

A: Find the dot product A∙ B and its angle of the given vectors: A = 10î - 4ĵ +7 k̂ and B = -2î +ĵ +…

Q: The angle that the x-axis make with the plane containing the following two vectors is A = 4â – 3 B =…

A: To find the angle

Q: Given the vector A= 5ax +3ay -7az and B= 3ax +6ay-2az, find (a) a unit vector in the direction of…

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Q: Given vectors A = 2a, + 4a, + 10a, and B = - Sa, + a, - 3a,, find (a) A + B at P(0, 2,-5) (b) The…

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Q: Given 2D vectors a and b such that |a|= 7 and |b| = 8 find the angle between the vectors if: a) |a…

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Q: Find the following for the vectors v = - 9i + j and u = - 5i + V3j. a. v•u, Įv], and |u| b. the…

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Q: The angle between vector A =4ax+5ay+6az and B = 3ax -2ay + 4az is * O 68.75 degrees O 56.62 degrees…

A: Angle between two vectors

Q: Here is a drawing of vectors a, b, and c. 18 ć Which equation correctly describes a in terms of b…

A: Given drawing of three vectors.

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

A: It is known that any two vectors are orthogonal if their dot product is zero. The given vectors are…

Q: For the given vectors a and b, find the cross product a x b. =(3,0, -1), b = (3, 2, 0) a %3D a x b =

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Q: Find the vectors T, N, and B at the given point. (1, 3 1) r(t) = T = N = B =

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Q: Find a vector B for which that is parallel to A =-6i +3j –2k but has the opposite direction.

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Q: Find the vectors T, N, and B at the given point.

A: Given vector and a point To find tangent vector T(t) use formula

Q: Q3: Find the angle between two vectors in space A = 41 - 2J-k B = 4T - 2J + 4k and

A: We need to find the angle between vectors A=4i¯-2j¯-k¯  and B=4i¯-2j¯+4k¯ for this we will use the…

Q: For the given vectors below, Solve for Vector č = (Ã+ B) × (÷ (B × Â)) %3D A = 3i+2j - 6k B = 31 -…

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Q: Given the vectors M = -10ax+4a, – 8a, and N= 8ax+ 7a, – 2a-, find: (a) a unit vector in the…

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Q: Find the angle a between the vectors L3] and]

A: Find the angle between vector s

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.…

Magnitude

A vector is an element with both direction and magnitude. A vector is represented using an arrow, where the arrow represents the direction of the vector and its length is represented using the magnitude. The set of vectors in space is known as vector space. The vectors can be added, subtracted, multiplied, and divided in a vector space. The image below shows a vector AB.