CBSE Class 11-science Answered

Find the component of 2i+3j along the direction of i+j and i-j.

Asked by prabal | 30 Sep, 2018, 02:04: PM

Expert Answer

begin mathsize 12px style L e t space a with rightwards arrow on top space equals space 2 space i space plus space 3 space j space comma space space b with rightwards arrow on top space equals space i space plus space j space comma space space c with rightwards arrow on top space equals space i space minus space j end style

To get the component of vector-a along the direction of vector-b, we need to find the angle between vector-a and vector-b.

The angle between the two vectors are determined using dot product.

begin mathsize 12px style a with rightwards arrow on top times space b with rightwards arrow on top space equals space 2 plus 3 space equals 5 semicolon space cos theta space equals fraction numerator a with rightwards arrow on top times space b with rightwards arrow on top over denominator space open vertical bar a with rightwards arrow on top close vertical bar space open vertical bar b with rightwards arrow on top close vertical bar end fraction space space equals space fraction numerator 5 over denominator square root of 13 space cross times square root of 2 end fraction space equals space fraction numerator 5 over denominator square root of 26 end fraction end style

hence component of vector-a along the direction of vector-b is,

begin mathsize 12px style fraction numerator 5 over denominator square root of 26 end fraction open parentheses 2 space i space plus space 3 space j close parentheses end style

Similarly we can get the component of vector-a along the direction of vector-c is,

begin mathsize 12px style open parentheses fraction numerator negative 1 over denominator square root of 26 end fraction close parentheses open parentheses 2 space i space plus space 3 space j close parentheses end style

Answered by Thiyagarajan K | 01 Oct, 2018, 09:07: PM

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