Consider two vectors: E₁ with magnitude 7 N/C and at an angle of 20 degrees above the positive direction, and E2 with magnitude 5 N/C and at an angle of 30 degrees to the left of the positive y direction. (a) Visualizing vector sums: Draw a vector sum diagram illustrating the sum EN = E₁ + E₂ and another of the vector difference E₁ = EN -E2. Make sure to label your arrows. Please make the diagram as close to scale as possible (use a ruler to measure, or use a program that lets you draw accurately.) - (b) Interpreting vector diagrams: From the diagram, should the magnitude of the sum be larger or smaller than 7 N/C? From the diagram, predict the general direction of the sum, within 1/8 of a circle (for instance, between 0 and 45 degrees above the x axis, etc.) Note, this is one good way to check your own answers when working with vectors.

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Problem 2. Vectors y 0, X Consider a vector E pointed into the second quadrant' of the Cartesian x-y coordinate plane, as pictured above. Consider the vector E pictured above and assume it is meant to represent some physical vector quantity we're studying. Since I've not specified what sort of physical quantity this vector is supposed to represent (perhaps it might be a force vector, a velocity vector, etc.), we'll leave it vague (but also recognize that the numerical values we record for physical quantities typically have units of measurment) and we'll just say that its units are simply called units. Suppose the magnitude, E, of E is given by E = 30.00 units, and suppose the angles drawn in the above figure are given by 0 = 60.00° and ø = 30.00°. (a.) What are the x- and y-components of vector E, pictured above, in terms of the angle 0 and the magnitude E? (b.) For the same vector, what are the x- and y-components in terms of the angle o and the magnitude E? (c.) What would these…

Consider vector A, with a magnitude of 3, and a vector B, with a magnitude of 2. Are the following relationships possible? If so, sketch a picture that shows an example of how they're possible, and identify all the angles between the vectors that make the relationship possible. (Exact angles, not decimal approximations. No calculators.) Relationship: Possible? Sketch: Angles: a. 1A+삐>5 b. A+ B| = 5 c. A+ B| = 1 d. A+미<1 - 1<|A+삐<5