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Grade: 12
        
define the scalar and vector product of two vectors a and b. if for three non zero vectors a, b and c, a.b=a.c and a*b=a*c then show that b=c.
 
10 months ago

Answers : (2)

Arun
14827 Points
							Scalar product is a special technique of multiplying two vectors. As the name suggests, we get a scalar quantity after multiplication. Scalar product is also known as dot product (since it is denoted by a dot between the vectors) or inner product. This is an operation which intakes two vector quantities and returns a single scalar quantity after the multiplication. The scalar product can be found either geometrically or algebraically
						
10 months ago
Shashank Singh
askIITians Faculty
57 Points
							a.b= ab cos<theta>
a.c=ac cos<phi>
cos<theta>= c/b cos<phi>............. (1)
similarly
Ia*bI= ab sin<theta>
Ia*cI= ac sin<phi>
sin<theta>=c/b sin<phi>.................. (2)
on squaring and adding (1) and (2), we get
1= c^2/b^2
c^2= b^2
so c=b.......... [ans}

10 months ago
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