Question

. If a = mb + c . The scalar m is
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Answer 1

Given:

a = mb + c .  

To find:

If a = mb + c . The scalar m is

Solution:

From given, we have,

a = mb + c  

as a, b and c are the vectors, so we have to take the dot product of b on both the sides,

a . b = m (b . b) + c . b

(we take dot product, in order to convert the vector "b" associated with a scalar m as a scalar "b²")

we use the dot product property a . a = a², so we get,

a . b = m (b²) + c . b

a . b - c . b = m (b²)

we use the dot product property a . b = b . a, so we get,

a . b - b . c = m (b²)

m = (a . b - b . c)/b²

∴ The scalar m is (a . b - b . c)/b²