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Question: In a clockwise system A. \(\hat{k}\times \hat{j}=\hat{i}\) B. \(\hat{i}\centerdot \hat{i}=0 \) ...

In a clockwise system
A. k^×j^=i^\hat{k}\times \hat{j}=\hat{i}
B. i^⋅i^=0\hat{i}\centerdot \hat{i}=0
C. j^×j^=i^\hat{j}\times \hat{j}=\hat{i}
D. k^⋅i^=1\hat{k}\centerdot \hat{i}=1

Explanation

Solution

There are two types of quantities; vector quantities and scalar quantities. Vector quantities have two ways through which product between two vector quantities can be obtained; one is dot product and the other is cross product. Dot product is commutative while cross product uses determinants.

Complete answer:
There are two types of quantities: Scalar and vector. Scalar quantities only have magnitude and do not have a specific direction to them. Examples of scalar quantities are distance, speed and temperature.Vector quantities are the type of quantities which have a magnitude as well as direction. Examples of vector quantities are velocity, displacement, force and many more. Vector quantities have vector products which are of two types; dot product and cross product.

Dot product shows the commutative property of multiplication while cross product is the determinant of the variables. Here, i, j and k are the unit vectors, and thus here, as i and i are in the same direction, their dot product is 1 and dot product of k and i is zero as they are in the opposite direction. The cross product of j and j should be zero as they are in the same direction. As the system is clockwise, the cross product of k and j is i as they are perpendicular to each other.

Hence option A is the correct answer.

Note: When the vectors are in the same direction, then their cross product is equal to zero while their cross product is equal to one and if two vectors are in a direction which is perpendicular to each other, then their dot product is equal to zero and cross product is equal to 1 or -1 depending upon clockwise and anti-clockwise situation.