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- It can be show that a plane area may he represented by a vector A=A, where A is the area and represents a unit vector normal to the piano: of the area. Show that the area vector of the parallelogram formed by the vectors a and b shown in the figure is A=ab.Given r=4i6j+2km (position vector) F=20i+40j30kN (force vector) =0.8j+0.6k (dimensionless unit vector) compute (a) rF; and (b) rF.The length of the position vector r is 240 mm. Determine the rectangular components of (a) r; and (b) the unit vector directed from O toward A.
- A circular region of radius R/2 is cut out from the circular region of radius R as shown. For what distance d will kx for the new region be the same as kx (for the region before the cutout was removed?1. Vector 1 is 30 m/s at 300° and Vector 2 is 80 m/s at 50°. Direction at CCW due East.a) Calculate the resultant vector using Pythagorean theorem and/or trigonometry.Find the projection of the vector A=-2j+k^ on the vector B= 6i+4 j+8k^
- A force F is represented by the vector 3i+4j+5k. Find the component of force F acting perpendicular to a plane, thi, which contains the vectors P=i-j, and Q=i+j-k (P and Q lie on thi).Find the resultant of two forces: A= 150N, acting 30 degrees to left of the y-axis, and B=100N, acting 40 degrees below the x-axis. * Your answern this question, you will calculate the second moment of area for a 4 ✕ 6 piece of lumber about the x − x and y − y axes, as shown. A rectangle with height h and width w > h is centered on the origin of the x y-coordinate plane. The left and right sides of the rectangle, having height h, are parallel to the vertical y – y axis and the top and bottom sides, having width w, are parallel to the horizontal x – x axis. Visit a hardware store and measure the actual dimensions of a typical 4 ✕ 6 piece of lumber. (Enter your answers in inches.) h = in w = in Calculate the second moment of area about the x − x and y − y axes using the measured dimensions. (Enter your answers in in.4.) Ix – x = ______in4 Iy – y = ________in4