First slide

Direction ratios and direction cosines

Question

Angle between the lines whose direction ratios are a,b,c and $b - c, c - a, a - b$ is

Moderate

A

$30^{0}$
B

$60^{0}$
C

$45^{0}$
D

$90^{0}$

Solution

$a_{1} a_{2} + b_{1} b_{2} + c_{1} c_{2} = 0$
a(b-c)+b(c-a)+c(a-b)=ab-ac +bc-ca+ca-ab=0

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