Which statement is true about the unit vectors L j and k? The directions defined

Question

Which statement is true about the unit vectors L j and k? The directions defined by a left-handed coordinate system. The angle between any two is 90 degrees, c Each has a length of I m. If i is directed east and j is directed south, k points up out of the surface. All of the above. If vector C is added to vector R the result is -9i - 8j If B b subtracted from G the result b What is the direction of B (to the nearest degree)? A vector A is added to B = 6i - 8j. The resultant vector is in the positive x direction and has a magnitude equal to A What is the magnitude of A? Exhibit 3-1 The three forces shown act on a particle.

Explanation / Answer

6.ALL ARE TRUE so, All of the above

7.C+B = -9i-8j

C-B = 5i+4j

so, B =-14i -12j Direction is tan-1(12/14) = 40.6 degrees (and third quadrant)

= 270-40.6 = 229.4 degrees ~ 230 degrees , answer is Option C

8

Let A be xi+yj So,A+B = (x+6)i -8j, Magnitude is same as A and y =8 because vector is in X-Direction

Equating both magnitudes, (x+6)^2 =x^2, so, x =-3.

Magnitude of A is Sqrt(3^2+8^2) = 8.54, Option is d.

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