The component of a vector (i + j) along (i - j) is:
Correct answer: A. 0
- A. 0
- B. 1/√2 (i - j)
- C. 1/√2 (i + j)
- D. (i - j)/2
Explanation
Let A= (i + j) and B=(i - j). The unit vector of A = i + j / |(i + j)||(i + j)|= √12+12=2 so, the unit vector of (i + j) = i + j /√2 = 1/√2 x i +1/√2 x j The unit vector of B = i - j / |(i - j)||(i - j)|= √12+(-1)2= √1+1= √2the unit vector of (i - j)= i - j/√2= 1/√2 x i -1/√2 x j When the vector A is mapped along vector B it will result in a component equal to zero.
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About Rectangular Components
A vector is resolved into perpendicular horizontal and vertical components using trigonometric relations, usually as Ax = A cos θ and Ay = A sin θ when θ is measured from the horizontal. Questions involve signs in different quadrants, reconstructing a resultant from components, and using components to analyse equilibrium.
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