Calculate the given quantity if
a=[1,1,-2]
b=[3,-2,1]
c=[0,1,-5]
(a) 2a + 3b
(b) |b|
(c) a. b
(d) compab
(e) projab
(f) the angle between a and b (correct to the nearest degree)

a.

b. .

c.

d.

e.  

f.

Step-by-step explanation:

The vector representation of A,B,C  is written as

a=[1,1,-2]

b=[3,-2,1]

c=[0,1,-5].

a.To determine the scalar product of 2a+3b we have

we add component by component w arrive at

b. we determine the magnitude of vector b i.e |b|. since b=[3,-2,1]

.

c.a.b is the dot product of vector a and vector b.

d. to find the component of b on a we use the expression

where

Hence if we substitute values we have

but earlier a.b=b.a=-1

e. to find the projection of b on a we have the expression

If we substitute values we arrive at

also recall that earlier we calculated a.b=b.a=-1 and

Hence

Hence

f. to determine the angle between vector "a" and "b" we use

where ∝ is the required angle . If we substitute values into the expression we arrive at

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