= 2. At any point of the curve x Tangent vector 3 cos t, y = 3 sin (ii) Unit tangent vector
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- Evaluate the following unit vector multiplications: (?̂ ×?̂)⋅?̂ (?̂ ×?̂)×?̂ (?̂ ×?̂) ×?̂Describe two vectors and such that Have you considered all possibilities? (a) a + b = and a + b = c; Hint and and 07=0. □ ā=0. are perpendicular. are in the same direction. Pretend these are not vectors and solve. (b) a + b = à-b; 07=0. a and and O = 0. are in the same direction. are perpendicular.Given the following three vectors: A = -9î+7), B = -6î -10} and vector C has a magnitude of, |=9 and makes and angle of 0=297°. Determine: a) D = A - C + 3B and D b) The angle that vector D makes with respect to the positive "x" axis.
- Vector A = (8, 4, -5) and Vector B = (-2, 3, 0). Find the angle between these two vectors.Two vectors A⃗ and B⃗ are at right angles to each other. The magnitude of A⃗ is 2.00. What should be the length of B⃗ so that the magnitude of their vector sum is 5.00?A vector is given as follows: =-37 -27-37 The vector product 7 *7 equals: O A. +37 + 37 O B. +37 + 27 - 31 OC-37 - 27 + 37 D.437 - 37 OE.-37 +37
- 14. The components of two vectors A and B are given as A, = 3, A, = -4, B, = -3, B, 3. IfC=A+ B, what is the magnitude of the vector C 4. 24 A) 0 B) 1 C)+1 D) -7 C+1D) -7 E E) none of the above 2√37 +132 JAX √(3)² + (-4) (31-4) = 5A vector has a magnitude of 2.8 m and points in a direction that is 135 counterclockwise from the a axis. You may want to review (Page 71).The vector has length 16 and points at an angle of 15° The vector 7 has length 12 and points at an angle of 40° -=
- 37. Go The components of vector A are A, and A, (both positive), and the angle that it makes with respect to the positive x axis is 0. Find the angle 0 if the components of the displacement vector A are (a) A, = 12 m and A, = 12 m, (b) A, = 17 m and A, = 12 m, and (c) A, = 12 m and A, = 17 m. %3D0 аф sin þa, + tan— Înr aº at P(2‚ñ/2,3/2). Determine If A = r sin 0 cosa, - cos 20 sin þaŋ + tan cos 20 the vector component of A that is parallel to az (express your answer in spherical coordinates)Two vectors a and 6 have magnitudes 4 and 2 respectively. Also the angle between a and bis Find a .. 130