Vectors Introduction Worksheet Unit 1 MCV4U Complete Solution

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Q1. A camera is suspended by two wires over a football field to get shots of the action from above. At one point, the camera is closer to the left side of the field. The tension in the wire on the left is 1500 N and the tension in the wire on the right is 800 N. The angle between the two wires is 130˚. Determine the approximate magnitude and direction of the resultant force.

Q2. Three forces act on a body. A force of 100 N acts towards the north, a force of 120 N acts towards the east, and a force if 90 N acts at N20˚E. Determine the resultant.

Q3. A ship’s course is set at a heading of 143˚ at 18 knots. A 10-knot current flows at a bearing of 112˚. What is the ground velocity of the ship?

Q4. Write each force as an algebraic vector in component form:
a. 500 N applied at 30˚ to the horizontal. b. 25 N applied downwards.

Q7. Determine the angle between the vector PQ and the positice x-axis, given endpoints P(4, 7) and C(8, 3).

Q8. Determine the value(s) of k such that u and v are orthogonal vectors.
a. u = (4, 1, 3), v = (-1, 5, k). b. u = (11, 3, 2k), v = (k, 4, k).

Q9. Find a vector that is orthogonal to both u = (2, 3, 1) and v = (4, 5, -2).

Q10. Find a unit vector that is orthogonal to both u = 3i – 4j +k and v = (2, 3, -4). #GCSE #SAT #EQAO #IBSLmath

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