3. Three vectors extending from the origin are given as r1 = 7a,+ 3a, – 2a,, r2 = -2a, + 7а, — За, and rg %3D 2а, - 2а, + За,. Find: A. A unit vector perpendicular to both r, and r2; B. A unit vector perpendicular to the vectors r1 – r2 and rą - r3i C. The area of the triangle defined by r, and r_; D. The area of the triangle defined by the heads of r, r2 and r3.

Algebra and Trigonometry (MindTap Course List)
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Chapter9: Vectors In Two And Three Dimensions
Section9.CR: Chapter Review
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3. Three vectors extending from the origin are given as r1 = 7a, + 3a, – 2a,, r2 = -2a, +
7ay - 3a,, and r3 = 2a, – 2a, + 3a,. Find:
A. A unit vector perpendicular to both r, and r2;
B. A unit vector perpendicular to the vectors r1 – rz and rɔ – rz;
C. The area of the triangle defined by r, and r,;
D. The area of the triangle defined by the heads of r, r2 and r3.
4. Four 3 pC charges are at the corners of a 1-m square. Two charges on the left are positive and the
other two on the right are negative. Find the E field at the center of the square.
5. The electric field at a distance r from a point charge Q = 125 fC is 11.2 V/m. Find the distance r and the
force on a point charge of 50 fC at a distancer.
6. Point charges 5 nC and-2 nC located at (2, 0, 4) and (-3, 0, 5) respectively. Determine the force on a 1 nC
point charge located at (1, -3, 7). Find the electric field at the same point.
Transcribed Image Text:3. Three vectors extending from the origin are given as r1 = 7a, + 3a, – 2a,, r2 = -2a, + 7ay - 3a,, and r3 = 2a, – 2a, + 3a,. Find: A. A unit vector perpendicular to both r, and r2; B. A unit vector perpendicular to the vectors r1 – rz and rɔ – rz; C. The area of the triangle defined by r, and r,; D. The area of the triangle defined by the heads of r, r2 and r3. 4. Four 3 pC charges are at the corners of a 1-m square. Two charges on the left are positive and the other two on the right are negative. Find the E field at the center of the square. 5. The electric field at a distance r from a point charge Q = 125 fC is 11.2 V/m. Find the distance r and the force on a point charge of 50 fC at a distancer. 6. Point charges 5 nC and-2 nC located at (2, 0, 4) and (-3, 0, 5) respectively. Determine the force on a 1 nC point charge located at (1, -3, 7). Find the electric field at the same point.
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