Question

a) Consider the force vectors A = 3i - 2j + 4k; B = 6i + 2j - 5k and C = -9i + 8j + 7k all expressed as Newtons. Determine the magnitude of -4A + 3B + 5C in N. b) The vector R = 5A + 5B + 9C where A = 3i - 3j + 7k; B = 9i + 9j - 8k and C = -8i + 4j + 3k all expressed as m. Determine theta-x, the angle R makes with respect to the x-axis in degrees. Abide by the 'right-hand rule' for the sign of theta-x. c) Consider two cables, one stretched between the 'origin' and Point A and the other stretched between the origin and Point B where the coordinates of Point A = (7, -8, 8) and of Point B = (7, 5, -8). Determine the magnitude of the angle between the two cables in degrees.

          a) Consider the force vectors A = 3i - 2j + 4k;
B = 6i + 2j - 5k and C = -9i + 8j + 7k all expressed as Newtons. Determine the magnitude of -4A + 3B + 5C in N.
b) The vector R = 5A + 5B + 9C where A = 3i - 3j + 7k; B = 9i + 9j - 8k and C = -8i + 4j + 3k all expressed as m. Determine theta-x, the angle R makes with respect to the x-axis in degrees. Abide by the 'right-hand rule' for the sign of theta-x.
c) Consider two cables, one stretched between the 'origin' and Point A and the other stretched between the origin and Point B where the coordinates of Point A = (7, -8, 8) and of Point B = (7, 5, -8). Determine the magnitude of the angle between the two cables in degrees.

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Added by Erin H.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Madhur L

07/20/2023

Step 1

-4A = -4(3 i - 2 j + 4 k) = -12 i + 8 j - 16 k 3B = 3(6 i + 2 j - 5 k) = 18 i + 6 j - 15 k 5C = 5(-9 i + 8 j + 7 k) = -45 i + 40 j + 35 k Now, let's add these vectors together: -4A + 3B + 5C = (-12 i + 8 j - 16 k) + (18 i + 6 j - 15 k) + (-45 i + 40 j + 35 k) = Show more…

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a) Consider the force vectors A = 3i - 2j + 4k; B = 6i + 2j - 5k and C = -9i + 8j + 7k all expressed as Newtons. Determine the magnitude of -4A + 3B + 5C in N. b) The vector R = 5A + 5B + 9C where A = 3i - 3j + 7k; B = 9i + 9j - 8k and C = -8i + 4j + 3k all expressed as m. Determine theta-x, the angle R makes with respect to the x-axis in degrees. Abide by the 'right-hand rule' for the sign of theta-x. c) Consider two cables, one stretched between the 'origin' and Point A and the other stretched between the origin and Point B where the coordinates of Point A = (7, -8, 8) and of Point B = (7, 5, -8). Determine the magnitude of the angle between the two cables in degrees.

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Transcript

00:01 Hello students, in the first part of the question, the question is minus 4a plus 3b plus 5c.

00:09 The vectors a, b and c are given in the question.

00:13 So on finding out this, we can substitute those values as minus 4 into a is given as 3i minus 2j plus 4k plus 3 into b vector is given as 6i plus 2j minus 5k plus 5 into c vector is minus 9i plus 8j plus 7k.

00:43 So here we will get the answer that is a resultant vector as minus 39i plus 54j plus 14k.

00:55 Now let's find out the magnitude of the resulting vector which will be equal to whole root of minus 39 square plus 54 square plus 14 square.

01:13 So we will get the magnitude of r as 68 .09 newton.

01:19 Now for the second question, let's find out 5a plus 5b plus 9c first.

01:29 Therefore, the resultant vector will be equal to 5 into the a vector is 3i minus 3j plus 7k plus 5 into 9i plus 9j minus 8k plus 9 into minus 8i plus 4j plus 3k.

01:53 So finding out the resultant vector, we will get the answer as minus 12i plus 66j plus 22k.

02:04 Now let's find out the theta value that is we know that tan theta x is equal to the components of the resultant vector along the x -axis divided by the components of the resultant vectors along the y -axis.

02:29 So the components will be that is theta x will be equal to tan inverse of minus 12 by the y component is 66.

02:41 So here we will get the theta value as minus 10 .11 degree...

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