For three vectors, find the magnitude and direction of the vector D A-B+ 3C. A o

Question

For three vectors, find the magnitude and direction of the vector D A-B+ 3C. A of leng 6.5 and pointing 56° up from the negative-x axis, B of length 6.7 and pointing 32° up from the positive-x axis, and C of length 2.8 and pointing 55° down from the positive-x axis. 10.-/1 pointsKatzPSEr1 3.P.021.MI Two aircraft approaching an aircraft carrier are detected by radar. The first aircraft is at a horizontal distance of 34.0 km in the direction 44.0° north of east and has an altitude of 2.30 km. The second aircraft, at half this altitude, is at a horizontal distance of 42.8 km in the direction 22.0° north of east. What is the distance separating the two aircraft? Hint: Use a coordinate system with the x axis pointing east, the y axis pointing north, and the z axis in the vertical direction. km Need Help? ReadItMaster it

Explanation / Answer

A = 6.5 (- cos56 i + sin56 j)

A = -3.63 i + 5.39 j

B =6.7 ( cos32 i + sin32 j)

B = 5.68i + 3.55j

C = 2.8 ( cos55i - sin55j)

C = 1.61 i - 2.29j

D = A - B + 3C

D = -4.48 i - 5.03 j

magnitude = sqrt(4.48^2 + 5.03^2)

= 6.7 .......Ans

Direction = tan^-1(5.03 / 4.48) = 48 deg below the -ve x axis. .....Ans

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