implies ui u balso calld eermne tne Solution5 a angle betwee

implies ui u balso calld eermne tne

Solution

5)

(a)

angle between the vectors =cos^-1[(<1,7>.<1,1>)_{/(1²+7²)(1²+1²)}]

angle between the vectors =cos^-1[((1*1)+(1*7))_/(1+49)(1+1)]

angle between the vectors =cos^-1[8_/502]

angle between the vectors =cos^-1[8_/100]

angle between the vectors =cos^-1[8_/10]

angle between the vectors =cos^-1[4_/5]=36.87^o

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(b)

angle between the vectors =cos^-1[((-5i+12j)(3i+2j))_{/((-5)²+12²)(3²+2²)}]

angle between the vectors =cos^-1[((-5*3)+(12*2))_{/(25+144)(9+4)}]

angle between the vectors =cos^-1[(-15+24)_/16913]

angle between the vectors =cos^-1[9_/(1313)] =78.93^o

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6)

a)

<3,4>.<6,8>

=(3*6)+(4*8)

=18+32

=50

so vectors are not orthogonal

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b)

(-4i+3j).(8i-6j)

=(-4*8)+(3*-6)

=-32-18

=-50

so vectors are not orthogonal

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7)

wz=(2+3i)(-4-i)

wz=2(-4-i) +3i(-4-i)

wz=(2*-4)-2i +(3i*-4)+(3i*-i)

wz=-8-2i -12i-3i²

wz=-8-14i-(3*-1)

wz=-8-14i+3

wz=-5-14i