Q3 - A//Find the value of M such that the vectors A 2i+ Mj+k and B = 4i-2j-2k %3D are perpendicular (20 marks)

Q: 02. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

A: Please refer the attached image for complete solution.

Q: 1.) Find the area of the parallelogram with vectors as adjacent sides. и %3D (-2,9, —3) аnd v %3D…

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Q: 4. Find the value of t such that the vectors ~v = h2t + 1,-3,3t - 2i and w = h7,4t +2,2i are…

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Q: . For what values of c are the vectors [−8, c, 4] and [c, c^2, c] orthogonal?

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Q: Are the three vectors: Ū;=4i-8j+k,V=2i+ J-2K and Ūz =3 i-4 j+12K in the Same Plane?

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Q: Q1. Given three vectors A = -a,+2a,+3a, B = 3a,+4a,+5a, and C = 2a, -2a,+7a,, compute : a) Angle…

A: Given the vector A=-ax+2ay+3azB=3ax+4ay+5azC=2ax-2ay+7az

Q: Q1, Find Parame tric equations for the line through the Point (0,1, 2) that is U =i +2} + 3k and ū=…

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

Q: 2. The two unit vectors parallel to the line 3x + 4y = 1 are and 3. The two unit vectors…

A: 2) The line is 3x+4y=1. Rewrite the equation of the line in the slope intercept form as,…

Q: Find the value of  x  so that the two vectors  (27,1,13)  and   (x,0,1)  are orthogonal

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Q: Find two unit vectors that are parallel to the yz-plane and are orthogonal to the vector 10i – 2j +…

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Q: Consider vectors, 2 u = |2, v = w = |-3 (a) Do these vectors line in a plane ? Why? Why not? Find…

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Q: Q5) Answer true or false for the followings: i) in triple dot of vectors |(A × B).C| = |(C × A). B|,…

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Q: The dot product of two vectors X1 y1 y2 and y = X2 Xn Yn ... 18

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Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. 1 Find the unit vector…

A: Given, X = -i + 3j  and Y = 4i -2j + 2k

Q: 02. Approve that the area of the parallelogram spanned by the vectors a- (2, -2, 1) and c= (-8, 8,…

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Q: Construct the vectors a = 3k - 2j and b = 3i - 2j and c = ax b. Compute the absolute value of the…

A: Given data : a⇀=3k-2jb⇀=3i-2j To calculate c=a×b The value a×b=ijk0-233-20

Q: Find the angle between the vectors u = /2i - 9j and v =v2i+j-2k.

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Q: Two vectors (M = 4ax-bay) and (N = 6ax-2ay-Saz), find the vector perpendicular to these vectors?

A: Given Vectors are                                                 M=4ax-6ayN=6ax-2ay-5az vector…

Q: Find the value of k for which the vectors 2 1 2 and -3 5 k are orthogonal. k =

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Q: 9. Find all the vectors with the length 6 units, which a = 2į +3j- 2k andh = i - 2j + 3k .…

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Q: 2. Determine the value of a for which the vectors b = ai – 5j+3k and 7 =i +2}-ak are orthogonal ?

A: Orthogonal Vectors: two vectors are orthogonal if they are perpendicular to each other. i.e. the dot…

Q: Determine n so that the vectors m = (-2, 1, k + 1) and n = (0, 2, -3) are parallel but in the…

A: It is assumed that the question asks to find the value of k for which the vectors will be parallel…

Q: 19. Show that the pair of vectors 8i+j and i-8j is perpendicular.

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Q: Express the vector - 4i - 8j + k as a product of its length and direction. - 4i - 8j + k=[Di+ ()j+…

A: To express the vector -4i-8j+k as a product of its length and direction.

Q: The unit vector which is perpendicular to both r1=8ax+3ay-2az, * r2=2ax+7ay-6az is equal to a)…

A: Given That: The unit vector is perpendicular to r1=8ax+3ay-2az & r2=2ax+7ay-6az

Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Given: u=23, v=k+1k-1 Concept Used: If two vectors are orthogonal then their dot product is zero.

Q: Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. -Y. 3. Find the unit vector…

A: Follow the procedure given below.

Q: Find all values of the scalar kfor which the two vectors are orthogonal.

A: Two vectors u and v are said to be orthogonal if u·v=0. Given that, u=1-12 and v=k2k-3 We have to…

Q: Q2. Approve that the area of the parallelogram spanned by the vectors a= (2, -2, 1) and c= (-8, 8,…

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Q: Decompose v into two vectors Vị and v2, where vi is parallel to w and v2 is orthogonal to w. v - -2i…

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Q: Q2 Given the vectors r=3i+4j-5k and s=-2J-K, where the xyz coordinate frame is obtained by rotating…

A: The given vectors are:r=3i+4j-5ks=-2j-k We have to find the cross product r×s

Q: -) THREE VECTORS A, B, AND C ARE RELATED AS FOLLOWS ! A AT 180°, A +C =-5+j15, 2 C = CONJU GATE OF…

A: Solution :-

Q: Find a so that the vectors v = i- aj and w = - 9i - 8j are orthogonal. (Type an integer or a…

A: As we know that; If two vectors v & w are orthogonal to each other then the dot product or…

Q: Q1:A-Find the equation of plane passes through (0,2,-1) parallel to the plane 3x+y+z=7? b- Find…

A: 1. A. According to question,Given plane,3x+y+z=7,Given Point 0, 2, -1

Q: 27-j+4k sī +2j-2k.

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Q: 2. (a) Compute ||(1,2, 3)||- (b) Find the angle between the vectors (1, v3) and (1,0).

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Q: State the condition that the two vectors i and y are perpendicular. Find the value(s) of k such that…

A: If two vectors are perpendicular to each other, then their dot product is equal to zero.

Q: 3. Consider the vectors X and Y in R³ where X = -i+3j and Y = 4i - 2j + 2k. Find the unit vector…

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Q: A n = i-j+3k, n2 = 2i +j+ 3k to the two vectors.

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Q: Let b = 4i + 3j and c be two %3D vectors perpendicular to each other in the xy-plane. All vectors in…

A: Given: b→=4i+3j and c→ are two vectors perpendicular to each other in xy-plane.  To find: All the…

Q: Find the vector projy 2i - 2j - 4k, u = 5i - 12 k

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Q: Find a so that the vectors v=i- aj and w = 7i- 10j are orthogonal. (Type an integer or a simplified…

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Q: Find a unit vector that is orthogonal to both >= 2i - 10j + 8k & v> = 4i + 6j – 8k Upload Choose a…

A: Explanation of the solution is given below...

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 vectors ü = 2î + 3j – 2k ö = -Sî - 2j – 7k w = 3î + j – 9k the value of [(- ü) x (u – w)].…

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

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Q: Find a vector 2 units long in the direction of v = 4i - j + 4k.

A: First find a unit vector in the direction of v = 4i - j + 4k.

Q: Let b = 4i + 3j and c be two vectors perpendicular to each other in the xy-plane. All vectors in the…

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Q: Find the angle 0 between the vectors a = 8i – j– 4k and b = 2i+j- 9k. %3D

A: A vector is a mathematical concept with both magnitude and direction. It's used to describe things…

Q: R) Find the area of a triangle formmed from the two - = c'+2j=k-- - 2i-jtuk. Vectors-a- 6 = 2i-j+4k,

A: Given: a=i^+2j^−k^b=2i^−j^+4k^