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Line has equation r= (3i-j+4k) + (-2i+j+2k) where is a calar. Line 12 has equation r= (7i-11j + 8k) +µ(2i +3j - 6k) where μ is a calar. Show that lines 1₁ and 1₂ meet, and find the coordinates of point P which is meir point of intersection.

Line has equation r= (3i-j+4k) + (-2i+j+2k) where is a calar. Line 12 has equation r= (7i-11j + 8k) +µ(2i +3j - 6k) where μ is a calar. Show that lines 1₁ and 1₂ meet, and find the coordinates of point P which is meir point of intersection.

Algebra & Trigonometry with Analytic Geometry
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter3: Functions And Graphs
Section3.3: Lines
Problem 31E
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8. Solve part A only
Line has equation = (3i − j + 4k) + 1(−2i+j+2k) where is a scalar. Line ₂ has equation r= (7i-11j +8k) +µ(2i +3j - 6k) where μ is a scalar. a) Show that lines and 1₂ meet, and find the coordinates of point P which is their point of intersection. e is the acute angle between lines 1₁ and 1₂. b) 1) Find cos 8, giving your answer in the form where c and d are integers. 4/17 ii) Show that sin 0 = 21
Transcribed Image Text:Line has equation = (3i − j + 4k) + 1(−2i+j+2k) where is a scalar. Line ₂ has equation r= (7i-11j +8k) +µ(2i +3j - 6k) where μ is a scalar. a) Show that lines and 1₂ meet, and find the coordinates of point P which is their point of intersection. e is the acute angle between lines 1₁ and 1₂. b) 1) Find cos 8, giving your answer in the form where c and d are integers. 4/17 ii) Show that sin 0 = 21
Point Q(1, 0, 6) lies on line and point R(17, 4,-22) lies on line 1₂. Find the area of triangle PQR. Give your answer in the form k√17 where k is an integer.
Transcribed Image Text:Point Q(1, 0, 6) lies on line and point R(17, 4,-22) lies on line 1₂. Find the area of triangle PQR. Give your answer in the form k√17 where k is an integer.
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