Question
Find the direction cosines of the sides of the triangle whose vertices are (3, 5, –4), (–1, 1, 2) and (–5, –5, –2).
Solution
Let A(3, 5, – 4), B(–1, 1, 2), C(–5, –5, –2) be the vertices of ΔABC.
Direction ratios of AB are – 1 – 3, 1 – 5, 2 + 4 i.e. – 4, – 4, 6
Dividing each by
cosines of the line AB as
i.e.
Direction ratios of BC are – 5 + 1, –5 –1, –2 –2 i.e. – 4, –6, –4.
Dividing each by
direction ratios of the line BC as
Direction ratios of CA are 3+5, 5+5, -4+2 i.e., 8, 10 -2.
Dividing each by
direction ratios of the line CA as
Direction ratios of AB are – 1 – 3, 1 – 5, 2 + 4 i.e. – 4, – 4, 6
Dividing each by
cosines of the line AB as
i.e.
Direction ratios of BC are – 5 + 1, –5 –1, –2 –2 i.e. – 4, –6, –4.
Dividing each by
direction ratios of the line BC as
Direction ratios of CA are 3+5, 5+5, -4+2 i.e., 8, 10 -2.
Dividing each by
direction ratios of the line CA as
