If A = A i and B = B j, then A . B is equal to:
Correct answer: B. Zero
- A. AB
- B. Zero
- C. 1
- D. AB k
Explanation
The value of a.b = 0. Step-by-step explanation: Given: a = ai and b = bj To find: The value of a.b Step 1 Let a = ai and b = bj Here a = ai Subtract ai from both sides, of the above equation, then we get a - ai = ai - ai Simplifying the equation, a - ai = 0 Factor a - ai: a - ai = 0 (1 - i)a = 0 Step 2 Using the Zero Factor Principle: If a.b = 0 then a = 0 or b = 0 a = 0 Step 3 Similarly b = bj Subtract bj from both sides, of the above equation, then we get b - bj = bj - bj Simplify b - bj = 0 Factor b - bj: b - bj = 0 (1 - j)b = 0 Therefore, the value of a.b = 0.
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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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