Given that A (-11:0),B(-3;4),C(3;p).calculate the value of p if A, B and C are collinear

Given:

a

=2

i

^

+

j

^

−3

k

^

and

b

=3

i

^

−2

j

^

−

k

^

a

.

b

=(2

i

^

+

j

^

−3

k

^

)(3

i

^

−2

j

^

−

k

^

)

=6−2+3=7(1)

∣

a

∣=

2

2

+1

2

+(−3)

2

=

14

(2)

∣

∣

∣

∣

b

∣

∣

∣

∣

=

3

2

+(−2)

2

+(−1)

2

=

14

(3)

cosθ=

∣

a

∣.

∣

∣

∣

∣

b

∣

∣

∣

∣

a

.

b

=

14

14

7

=

2

1

cosθ=cos60

o

θ=60

o

Hence the required angle is 60

o

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