Final answer:
The student's question involves resolving vectors into their scalar components and then performing vector sums and differences according to the given equations. To solve for R, D, and S, corresponding x and y components of the vectors need to be added or subtracted respectively. A dilated vector is created by multiplying its components by the given scale factor.
Step-by-step explanation:
The student's question is related to vector operations, specifically vector addition and subtraction in Mathematics. The operations must be carried out by first resolving each vector into its scalar components along the x and y axes. For vector B, with an angle of -110°, the horizontal and vertical components are Bx = -2.39 cm and By = -6.58 cm respectively. The question further requires performing the vector sums (a) R = A + B + C, (b) D = A - B, and (c) S = A - 3B + C, where the subtraction indicates a dilation by a factor of 3 and inverting the direction of vector B.
The procedure typically includes adding the corresponding scalar components of the vectors for sum operations, and subtracting them for the difference operations. For instance, if we have vector A with components Ax and Ay, to find R we would calculate Rx = Ax + Bx + Cx and Ry = Ay + By + Cy. Understanding the angles and their trigonometric associations is crucial to resolving these components correctly. Remember that dilating vector B by a factor of 3 means multiplying both components, Bx and By, by 3.
For the vector D which is A - B, simply subtract B's components from A's. For the operation involving S as in A - 3B + C, we need to triple B's components and then subtract them from A's components, before finally adding C's components to the result.