1. If ŌA = 4i + 3j, OB = 6i - 2j, OC = 2i-j, find AB, BC and CA, and deduce the lengths of the sides of the triangle ABC. %3D

Algebra and Trigonometry (MindTap Course List)
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ISBN:9781305071742
Author:James Stewart, Lothar Redlin, Saleem Watson
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Chapter9: Vectors In Two And Three Dimensions
Section9.CR: Chapter Review
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1. If ŌA = 4i + 3j, OB = 6i- 2j, OC = 2i-j, find AB, BC and CA, and
deduce the lengths of the sides of the triangle ABC.
2. If Ā = 2i + 2j-k and B = 3i- 6j + 2k, find (i) A.B and (ii) ĀXB.
3. Find the direction cosines of the vector joining the two points
(4, 2, 2) and (7, 6, 14).
4. If Ā = 5i + 4j + 2k, B = 4i- Sj +3k, and C = 2i-j- 2k, where i, j,
k, are the unit vectors, determine
(i) the value of Ā.B and the angle between the vectors A and B.
(ii) the magnitude and the direction cosines of the product vector
(ĀX B) and also the angle which this product vector makes
with the vector C.
Transcribed Image Text:1. If ŌA = 4i + 3j, OB = 6i- 2j, OC = 2i-j, find AB, BC and CA, and deduce the lengths of the sides of the triangle ABC. 2. If Ā = 2i + 2j-k and B = 3i- 6j + 2k, find (i) A.B and (ii) ĀXB. 3. Find the direction cosines of the vector joining the two points (4, 2, 2) and (7, 6, 14). 4. If Ā = 5i + 4j + 2k, B = 4i- Sj +3k, and C = 2i-j- 2k, where i, j, k, are the unit vectors, determine (i) the value of Ā.B and the angle between the vectors A and B. (ii) the magnitude and the direction cosines of the product vector (ĀX B) and also the angle which this product vector makes with the vector C.
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