Two vectors are given by a 4.0 m 3.0 m ) + (1.0 m ) and b = ( -1.0 m )i + (1.0 m )j + (4.0 m )k. k. In unit-vector notation, find (a) a + b, (b) ab, and (c) a third vector such that a b + c = 0. (a) Number (b) Number (c) Number i + + <·~ + + <•+ <•+ i i i k Units k Units k Units
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- The force F has a magnitude of 590 N. Express F as a vector in terms of the unit vectors i and j. Identify the x and y scalar components of F. Assume F = 590 N, 0 = 31° Answers: F = (i Fx= i Fy || IM F i+ N N Mi INTwo vectors, r and s lie in the xy plane. Their magnitudes are 4.58 and 8.82 units, respectively, and their directions are 304° and 76.0°, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) r and (b) T x 3? (a) Number i -27.03 Units (b) Number i 30.02 UnitsTwo vectors, ŕ and s lie in the xy plane. Their magnitudes are 4.58 and 8.82 units, respectively, and their directions are 304° and 76.0°, respectively, as measured counterclockwise from the positive x axis. What are the values of (a) r ·S Š and (b) 7 x 3 ? (a) Number i Units (b) Number i Units
- 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 A has components Ax = −3.00 m and Ay = 6.00 m. Find the magnitude (in m) and the direction (in degrees counterclockwise from the +x-axis) of the vector.Three vectors V₁, V2, V3 originate from a single point. The vector v₁ is on the x-y plane, at an angle of 30deg counter-clockwise from the positive x axis and has a magnitude of 500 units. The vector v₂ is on the y-z plane at an angle counter-clockwise from the positive y axis such than tan 0= 3/4 and has a magnitude of 400 units. Vector V3 has a magnitude of 800 units. If the direction of the resultant vector is defined by the unit vector Ug = cos 30º j + sin 30º k. (A) Determine the coordinate angles of v3. (B) Determine the magnitude of resultant vector. Report results in three significant figures.
- You are given 3 vectors: p = j - 3k, q = -2i - j - 3k and r = 4i + j + 3k. You are informed that these three vectors are Cartesian unit vectors. To answer this question, you must use the form: a1i + a2j + a3k Find a unit vector in the direction of qGiven vector A=2i-3j and vector B = 2i -4j. If vector C = A -2*B then C equals ..Vector CC has a magnitude of 22.222.2 m and points in the −?‑−y‑direction. Vectors AA and BB both have positive ?‑y‑components, and make angles of α=43.9°α=43.9° and β=27.2°β=27.2° with the positive and negative ?-x-axis, respectively. If the vector sum A+B+C=0A+B+C=0, what are the magnitudes of AA and B?