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3-1.Vectors
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કારણ સહિત જણાવો કે અદિશ તથા સદિશ રાશિઓ સાથે નીચે દર્શાવેલ કઈ પ્રક્રિયાઓ અર્થપૂર્ણ છે ?
$(a)$ બે અદિશોનો સરવાળો
$(b)$ સમાન પરિમાણના એક સદિશ અને એક અદિશનો સરવાળો
$(c)$ એક સદિશનો એક અદિશ સાથે ગુણાકાર
$(d)$ બે અદિશોનો ગુણાકાર
$(e)$ બે સદિશોનો સરવાળો
$(f)$ એક સદિશના ઘટકનો તે જ સદિશ સાથે સરવાળો.
Option A
Option B
Option C
Option D
Solution
$(a)$ Meaningful : The addition of two scalar quantities is meaningful only if they both represent the same physical quantity.
$(b)$ Not Meaningful : The addition of a vector quantity with a scalar quantity is not meaningful.
$(c)$ Meaningful : A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
$(d)$ Meaningful : A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
$(e)$ Meaningful : The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
$(f)$ Meaningful : A component of a vector can be added to the same vector as they both have the same dimensions.
$(b)$ Not Meaningful : The addition of a vector quantity with a scalar quantity is not meaningful.
$(c)$ Meaningful : A scalar can be multiplied with a vector. For example, force is multiplied with time to give impulse.
$(d)$ Meaningful : A scalar, irrespective of the physical quantity it represents, can be multiplied with another scalar having the same or different dimensions.
$(e)$ Meaningful : The addition of two vector quantities is meaningful only if they both represent the same physical quantity.
$(f)$ Meaningful : A component of a vector can be added to the same vector as they both have the same dimensions.
Standard 11
Physics