With vector alegbra, how would you plot such a vector on a coordinate plane as (-4 i-hat + 4 j-hat)?
by 
bobbybrown
ANSWERS: 3
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hat? is that supposed to be -4i + 4j? You simply put a point on (-4, 4) just like it's a Cartesian plane. The resultant magnitude is 4√2
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By 'hat' I assume you mean the symbol ^ , which when placed over i and j means UNIT VECTORS along two perpendicular axes. I'll write i^ and j^ to mean i-hat and j-hat. So it's similar to plotting the point (-4,4) on the x-y Cartesian plane. The numbers -4 and +4 are the vector's COMPONENTS. [edit] The unit vectors i^ and j^ go from the origin(0,0) to the points (1,0) and (0,1), respectively. (Sometimes you use -1.) The components are like a recipe. The vector from the origin (0,0) to the point (-4,4) is composed of -4 of i^ and +4 of j^. Since i^ = (1,0) then -4i^ = (-4,0) etc. When you take a vector of length 4 in the OPPOSITE direction of i^, and add it to a vector of length 4 ALONG the direction of j^, you get a vector at 45 degrees according to the parallelogram rule. Put differently, the vector from (0,0) to (-4,4) DECOMPOSES into -4i^ + 4j^. (also see LINEAR COMBINATION) The length of this vector is 4√2 using the Pythagorean theorem.
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so, will the be along the X and Y axi? and how do you calculate the magnitude and direction, given VectorC = (-4i^, 4j^)
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