Question

The component of vector ar = 2ˆi + 3ˆj along the vector
i + j is
(a)5/√2
(b) 10 √2
(c) 5 √2 (d) 5

Answer 1

Answer:

B

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Answer 2

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

So,B is the right answer.