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Home / Doubts and Solutions/ICSE/Class 11 Science/Physics

charactrastic of scalar product

 

Asked by pavanjadhao347 23rd October 2018, 10:43 AM
Answered by Expert
Answer:
Characteristic of scalar product or dot product
 
i) Scalar product obeys commutative law.
 
stack P. with rightwards arrow on top stack Q space with rightwards arrow on top equals space stack Q. with rightwards arrow on top stack P space with rightwards arrow on top
ii) Scalar product obeys distributive law.
P with rightwards arrow on top. left parenthesis stack space Q with rightwards arrow on top plus stack R right parenthesis with rightwards arrow on top equals stack P. with rightwards arrow on top Q with rightwards arrow on top plus space P with rightwards arrow on top. R with rightwards arrow on top
iii) In scalar product 
stack P. with rightwards arrow on top stack Q space with rightwards arrow on top space equals space P Q space cos theta 1 right parenthesis I f space theta equals space 0 to the power of ring operator T h e n comma space t w o space v e c t o r s space a r e space p a r a l l e l space P Q space cos space 0 to the power of ring operator equals space P Q 2 right parenthesis space I f space theta equals space 180 to the power of ring operator T h e n comma space t w o space v e c t o r s space a r e space a n t i space p a r a l l e l space P Q space cos 180 to the power of ring operator equals space P Q left parenthesis negative 1 right parenthesis space equals space minus P Q 3 right parenthesis I f space theta equals space 90 to the power of ring operator T h e n comma space t w o space v e c t o r s space a r e space p e r p e n d i c u l a r space t o space e a c h space o t h e r space left parenthesis i with hat on top. space j with hat on top equals space j with hat on top. space k with hat on top space equals space space k with hat on top. space i with hat on top space equals space 0 right parenthesis P Q space cos 90 to the power of ring operator equals space P Q left parenthesis 0 right parenthesis space equals space 0 space comma space w h e r e comma space P comma space Q space not equal to 0
iv) If 
P with rightwards arrow on top equals space stack Q space with rightwards arrow on top space T h e n space stack P. with rightwards arrow on top stack Q space with rightwards arrow on top space equals space P squared space equals space Q squared
 
v) If 
stack P space with rightwards arrow on top equals i with overbrace on top space P subscript x space plus space j with overbrace on top space P subscript y space plus k with overbrace on top space P subscript z stack Q space with rightwards arrow on top equals i with overbrace on top space Q subscript x space plus space j with overbrace on top space Q subscript y space plus k with overbrace on top space Q subscript z stack P space with rightwards arrow on top. stack Q space with rightwards arrow on top space equals space P subscript x Q subscript x space plus space P subscript y Q subscript y space plus space P subscript z Q subscript z
Answered by Expert 23rd October 2018, 11:56 AM
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Tags: dot-product scalar-product-of-two-vectors
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