Karteikarten
Vectors and Complex Numbers
Karten in diesem Stapel (27)
- 1Vector u has its initial point at (-7, 2) and its terminal point at (11, -5). Vector v has a direction opposite that of vector u, and its magnitude is three times the magnitude of u. What is the component form of vector v? A. v = <-54, 63> B. v = <-162, -63> C. v = <-54, 21> D. v = <-162, 21>C.
v = <-54, 21> - 2Vector u has its initial point at (17, 5) and its terminal point at (9, -12). Vector v has its initial point at (12, 4) and its terminal point at (3, -2). Find ||3u − 2v||. Round your answer to the nearest hundredth. A. 29.79 units B. 32.12 units C. 39.46 units D. 42.23 unitsC.
39.46 units - 3Vector u has its initial point at (14, -6) and its terminal point at (-4, 7). Write the component form of u and find its magnitude. u = <__, ___>, and ||u|| ≈ ___ units.<-18, 13>
22.2 - 4—C
- 5Write the component forms of vectors u and v, shown in the graph, and find v − 2u. u = __ v = __ v − 2u = __<2,2>
<0,-4>
<4,0>
- 6Vector u has a magnitude of 7 units and a direction angle of 330°. Vector v has magnitude of 8 units and a direction angle of 30°. What is the direction angle of their vector sum? A. 0° B. 2.20° C. 30° D. 357.80°B.
2.20° - 7Vector u has a magnitude of 5 units, and vector v has a magnitude of 4 units. Which of these values are possible for the magnitude of u + v? 1 unit 9 units 11 units 13 units1 unit
9 units - 8Consider the vectors u = <-4, 7> and v = <11,-6>. u + v = <__, __> ||u + v|| ≈ ___units7, 1
7.07 - 9Vector u has a magnitude of 5 units and a direction angle of 75°, and vector v has a magnitude of 6 units and a direction angle of 210°. What is the component form of the vector u + v? A. < -3.95, 1.83> B. < -3.94, 1.89> C. < -3.90, 1.89> D. < -3.90, 1.83>D.
< -3.90, 1.83> - 10If w = <3.5, -6> and z = <-1.5, -4>, what is the resulting vector for 2w − z? A. <5, -2> B. <10, -4> C. <8.5, -8> D. <5.5, 12>C.
<8.5, -8> - 11Which components are a possible representation of vector u if ||-4u|| ≈ 14.42? A. <3, -2> B. <-1, 4> C. <2, 2> D. <-2, -4>A.
<3, -2> - 12Find the results of the given vector subtractions for u = <-8, 4> and v = <2, 7>. -u – v = ___ u – v = ___ v – u = ___6,-11
-10,-3
10,3 - 13The resulting vector for w – z is <__, __>, and z – w is <__, __>.-7,-3
7,3
- 14—C
- 15If u = 3 − 4i and v = 3i + 6, what is u − v? A. -3 + 7i B. -3 − 7i C. 3 + 7i D. 3 − 7iB.
-3 − 7i - 16If (2 + 3i)2 + (2 − 3i)2 = a + bi, a = ___and b = __.-10,0
- 17—B
- 18Convert (2, pi) to rectangular form. A. (2, 0) B. (-2, 0) C. (0, 2) D. (0, -2)B.
(-2, 0) - 19Convert x^2 + y^2 = 16 to polar form. A. r = 16 B. r = 4 C. θ = 16 D. θ = 4B.
r = 4 - 20Convert (1, 1) to polar form. A. (2, 45°) B. (1, 45°) C. (2, 225°) D. (sqrt 2, 45°)D.
(sqrt 2, 45°) - 21Convert 3cis 180° to rectangular form. A. -3 B. -3i C. 3 D. 3iA.
-3 - 22—D
- 23Convert 5cis 270° to rectangular form. A. -5 B. -5i C. 5 D. 5iB.
-5i - 24Which graph represents the product of a complex number, z, and the negative real number -1/3 ?C
- 25The graph represents two complex numbers, z1 and z2, as solid line vectors. Which points represent their complex conjugates?A, L
- 26In the graph, z is a complex number represented as a vector from the origin. What is the product of z and its conjugate? The product of the complex number z and its conjugate is ___5
- 27Which operations involving complex numbers have solutions represented by point A on the graph? (4 + i) + 3(1 + i) (4 + i) − 3(1 + i) (4 + i) + (-3 − 3i) (4 + i) + (3 − 3i) (4 + i) − (3 + 3i)2nd
3rd
5th
Informationen
- Beschreibung
- - Vectors in a Plane - Velocity Vectors - Negative Vectors - Complex Numbers - Polar Coordinates in Graphs - Complex Numbers and DeMoivre's Theorem - Complex Numbers in the Plane
- Erstellt von
- Elexali Olayvar
- Aufrufe
- 6
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