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If you know cosine of an angle you can easily find sine of it as well as follows:Referred to the origin O, the points A, B and C have position vectors given by
−−→ OA = i + 2j + 3k, −−→ OB = 2i + 4j + k and −−→ OC = 3i + 5j − 3k.
(i) Find the exact value of the cosine of angle BAC. [4]
(ii) Hence find the exact value of the area of triangle ABC. [3]
(iii) Find the equation of the plane which is parallel to the y-axis and contains the line through B and C. Give your answer in the form ax + by + cÏ = d. [5]
Please help me with (ii), how do I get the sin of the angle sqrt41/21 as referred to mark scheme? My friend told me to use A^2=B^2+C^2, but how can we know if triangle ABC is a right-angled triangle? Is there any other way to solve this besides my friends method and sine rule?
ASAP. Thanks!!
sin^2(X) + cos^2(X) = 1
You probably know this identity already. Substitute what you know to find the other.