component of vector A =2i+3j along the direction of i-j is
Answers
i-j we should find the unit vector along i-j .
Detailed solution is in the attachment.
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Answer:
Component of vector A=2i+3j along the directionof i-j = - ½ i+ ½ j
Explanation:
According to the question, the component of vector A is to be found along direction of i- j, which is found by finding the unit vector of A along the same.
Given is that Vector A = 2i + 3j
Let us assume that the unit vector a along i- j
Thereby, vector a = ( vector along i – vector along j ) / |i- j |
Vector a = 1 / √ 2 ( vector i- vector j )
So, the component along the i- j will be the multiplication product of vector A and unit vector a.
Component of vector A = ( vector A. vector a ) vector a
Component = { ( 2i + 3j ) . 1 / √ 2 ( vector i- vector j ) } 1 / √ 2 ( vector i- vector j )
Component = 1 / √ 2 ( 2 – 3 ) 1 / √ 2 ( i- j )
Component = - 1 / √ 2 (1 / √ 2 ( i- j ) )
Component = - ½ i+ ½ j