Consider the kets: -3-2i] Irn) = -6i 5i [4i-71 ,Ir2) =9+8i y Ir3) = 4-5i [7i-4] 3 11 a) Calculate the scalar products (r|r2), (r2|r3) And (r3/ri). b) Normalize |r), Ir2) and Ir3). c) Consider zero the imaginary part of each component of the kets and again calculate a) and b).

Q: Find a linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

A: A linear mapping G that maps [0, 1]×[0, 1] to the parallelogram in the xy-plane spanned by the…

Q: Find a unit vector normal to the plane containing v=2i+3j-k and . w = -2i - 4j - 3k.

A: Given: v=2i+3j-k  w = -2i - 4j - 3k.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 5u . (3v - 4w)or vector.

A: It is given that  u = -i + j, v = 3i - 2j, and w = -5j

Q: Calculate the scalar triple product u · (v × w), where u =〈1, 1, 0〉, v =〈3, −2, 2〉, and w =〈4, −1,…

A: The vectors are, u=1,1,0v=3,-2,2w=4,-1,2 We need to find the scalar triple product u·v×w

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: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 3u - (4v - w)or scalar.

A: Concept:   The calculus helps in understanding the changes between values that are related by a…

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A: Given vector is v = -3i +7j.

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Q: Find the scalar and vector projections of b onto a, where a = (2, −2, 1) and b =  (IMAGE)

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar 4u . (5v - 3w)or vector.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j.Find specified scalar proju(v + w) or vector.

A: Here given vectors as u = -i + j, v = 3i - 2j, and w = -5j. Thus  v+w=3i-2j+-5jr(say)=3i-7j

Q: Let x = 8i – 5j - and y = 3j – 7k be two vectors. Find the value of the scalar product x · y.

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Q: . If u and v are nonzero vectors in Rº, why do the equa- tions u · (u x v) = 0 and v · (u x v) = 0…

A: The dot product of orthogonal vectors is equal to zero.

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A: Given a=3i-j+6k    b=j+12k

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Q: write the equation of the plane with normal vector n passing through the given point in the scalar…

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Q: Write the scalar equation of the plane with normal vector = [1, 2, 1)] and passing through the point…

A: here normal vector is  and the given point is

Q: Use properties of the cross product to find the area of the parallelogra nerated by the two vectors…

A: Recall: Area of the parallelogram form by two vector a and b is a×b

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Q: Find the scalar and vector projections of b onto a, where a = (1, 2) and b = (-4, 1). 1. comp, b 2.…

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Q: Can you find two vectors in R whose dot product is equal to their cross product? No, because the…

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Q: Let u = -2i + 3j, v = 6i - j, w = -3i. Find the specified vector or scalar lu + vl2 - lu - vl2.

A: The given vectors are  u=-2i+3j , v=6i-j  ,w=-3i To find: the value of u+v2-u-v2. Solution: Since,…

Q: Find the scalar and vector projections of b onto a. a = 3i - j + 6k,     b = j + (1/2)k compab =…

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Q: Write the equation of the plane with normal vector n = 4k passing through the point (7, 2, 5) in the…

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Q: Compute the orthogonal projection of u = form, not a decimal approximation. onto v= 3 2 Leave your…

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Q: Describe the loci zz−2z−2z+8 = 0 expressed in terms of conjugate coordinates z, z.

A: It is given thatzz¯-2z-2z¯+8=0Where,z¯ is the conjugate co-ordinate of z.We have describe the locus.

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Q: Let u = 2i - 5j, v = -3i + 7j, and w = -i - 6j.Find specified vector or scalar 5v.

A: Given vectors are u=2i-5j, v=-3i+7j and w=-i-6j. To find: The vector or scalar 5v. Solution: When we…

Q: Find the normal unit vector perpendicular on à and B for A = 2i+3j-k and B=-j+2k %3D

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A: Given , a = (0,1,-2) and b = (-1,0,3).

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

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Q: Find a linear mapping G that maps [0, 1] x [0, 1] to the parallelogram in the xy-plane spanned by…

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Q: Show with the help of the calculation rules for the scalar product for vectors ||x – 2 y|| = ||x||2…

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Q: find two distinct vectors on the line belonging to the intersection of the hyperplanes: Xi+ 2x2 - X3…

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Q: Let u = -2i + 3j, v = 6i - j, w = -3i.Find specified vector 4u - (2v - w)or scalar.

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Q: Let u = -i + j, v = 3i - 2j, and w = -5j. Find the specified scalar or vector: proju (v - w)

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Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.