If the unit vectors i, j, k are perpendicular to each other therefore;i.i = j.j = k.k = _.I.j = j.k = k.i = _.
Correct answer: B. 1 ... 0
- A. 0 ... 1
- B. 1 ... 0
- C. 0 ... 0
- D. 1 ... 1
Explanation
The dot product of two vectors A and B is given by A.B = |A||B| cosθ. If the angle θ between the vectors is 0°, cosθ = 1, so a vector dotted with itself (i.i, j.j, k.k) is 1, due to the unit magnitude of the vectors. If θ is 90°, cosθ = 0, so the dot product of two perpendicular vectors (i.j, j.k, k.i) is 0. Therefore, the correct answer is 1 for i.i = j.j = k.k, and 0 for i.j = j.k = k.i. The other options are incorrect as they do not accurately reflect these properties of the dot product for unit vectors.
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About Scalar Product
The scalar product of two vectors is A dot B equals AB cos theta, producing a scalar determined by their magnitudes and included angle. Applications include work done and projection of one vector on another, with perpendicular vectors giving zero and the scalar product distinguished from the vector product.
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