Q3: Express the vector A = 2√3i+ 3√3j-2√2k in the primed triad i'j'k' in which x'y'-axes are rotated about z-axis (which coincides with the z'-axis) through an angle of 30º.
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- Vector A = 7.2 i + 2.6 j. Vector B = 7.5 i + 7.4 j. The magnitude of the cross product i.e. |AxB| is: :Suppose that u and v are vectors in R'. Decide whether each statement is always true or not always true. Be sure you can explain why your answers are correct! + 1. ủ · ở = ở · ủ 2. ů xi = -(3 xủ) ? 3. (-ū) × (-i) = -u x i) 4) 4. (-i) = -α . b)Two vectors are given by 7 8.31 + 3.2) and B = 7.6i + 8.7, vind (o 7 x 7 | 7 7 (a + ). B. and (d) the component of 7 along the direction of ? (a) Number Units (b) Number Units (c) Number Units (d) Numberi Units
- Determine the cross product of the following vectors A x B, write the component in the j-direction. A=35 i + 97.4 j + 74.1 k B=86 i + 42.2 j + 26.8 kTwo vectors are given by A = 3i– 23 + 4k and B = 6} – 2k. Ignoring units, calculate Ả× B.Consider the two vectors A-5i-j and B = - i- 4j. (a) Calculate A+B i+ (b) Calculate A -R i (c) Calculate A+ E (d) Calculate A - E (e) Calculate the directions of A +B and A-B. * (counterclockwise from the +x axis) A - B * (counterclockwise from the +x axis)
- A force is specified by the vector F = [(100)i + (-110)j + (70)k] N. Calculate the angles made by F with the positive x-, y-, and z-axes. Answers: ex= i 0 0y = i 0₂ = i O▼ Part A What is the angle between vectors A and B if à = 2 î – 5 ĵ and B = −5 î + 7 ĵ? Express your answer in degrees. ► View Available Hint(s) 0 = Submit Part B 0 = 197| ΑΣΦ 6 What is the angle between vectors A and B if A = 2 î+43 and B = 8 î - 4 ĵ? Express your answer in degrees. ► View Available Hint(s) Submit ? || ΑΣΦ ? 0Vector v = <1,1,0> and vector w = <-1,-1,sqrt2>. What is the angle between v and w in degrees?
- q2Let's consider two vectors, A = (-7, 10), B = (-5, -8), and C = (-1, 6) as shown below. A C B What is the magnitude of A+ B+ C? Answer What is the direction (8) of A+B+C relative to +x-axis? a-839 b. 20 C-85 3 d. 148°What is the relation between A×B and BxA, The magnitudes are the same but they are in opposite directions, i.e., (Ã×B)=-(BxÃ) The order of the vectors in a cross product doesn't matter so they are the same, i.e., (ÃxB)=(BxÃ)