Referred to the origin O, the points A, B and C have position vectors given by OÅ = i + 2j + 3k, OB = 2i + 4j + k and oċ = 3i + 5j – 3k. %3D (i) Find the exact value of the cosine of angle BAC.

Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
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Chapter8: Applications Of Trigonometry
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Referred to the origin O, the points A, B and C have position vectors given by
OÁ = i+ 2j + 3k,
OB = 2i + 4j + k and OĆ = 3i + 5j – 3k.
(i) Find the exact value of the cosine of angle BAC.
(ii) Hence find the exact value of the area of triangle ABC.
(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 + cz = d.
Transcribed Image Text:Referred to the origin O, the points A, B and C have position vectors given by OÁ = i+ 2j + 3k, OB = 2i + 4j + k and OĆ = 3i + 5j – 3k. (i) Find the exact value of the cosine of angle BAC. (ii) Hence find the exact value of the area of triangle ABC. (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 + cz = d.
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