If A + B= 7i^ +7k^ and A-B= -i^ + k^, then the magnitude of A will be:
Correct answer: C. 5
- A. -1
- B. 3
- C. 5
- D. 7
Explanation
Given:A + B = 7i^ + 7k^A - B = -i^ + k^To find the magnitude of A, we need to eliminate B from these equations. We can do this by adding the two equations together:(A + B) + (A - B) = (7i^ + 7k^) + (-i^ + k^)Simplifying the left side and right side separately:2A = 6i^ + 8k^Dividing both sides by 2:A = 3i^ + 4k^Now we have the vector A. To find its magnitude, we can use the formula:|A| = √(Ax² + Ay² + Az²)In this case, Ax = 3, Ay = 0, and Az = 4. Substituting these values into the formula:|A| = √(3² + 0² + 4²)= √(9 + 0 + 16)= √25= 5Therefore, the magnitude of A is 5. Hence, option C is the correct answer.
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Vectors have magnitude and direction, unlike scalars, and are combined by head-to-tail or parallelogram methods. Work covers rectangular components, equilibrium when the resultant force is zero, the scalar product for work and projections, and the vector product for torque and cross-product direction using the right-hand rule.
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