The value of i cap x (j cap x k cap ) is
1) 0
(2) 1
(3) 2
(4) Cannot be found
( vectors: x means cross product, cap means unit vector)
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Answer:
(4) cannot be found..
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Given:
î×(ĵ×k̂)
To Find:
Value of the above vector-product expression.
Solution:
We know that î,ĵ & k̂ are rectangular unit vectors in the direction of the x-axis, y-axis, and z-axis respectively i.e. their magnitude is 1 and direction is along their respective axes.
We will first find out the vector product of ĵ & k̂.
Since the magnitude of each vector is 1 and has an angle of 90° between each of them, the cross product is going to have a magnitude of 1 and direction along the x-axis (using the Right-hand thumb rule)
So, ĵ×k̂=î
⇒ î×(ĵ×k̂)=î×î
Now, the angle between î and î is 0°
So, î×î=0 vector.
Hence the value of the expression î×(ĵ×k̂)=0 vector.
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