The angle between the lines whose direction cosines

The angle between the lines whose direction cosines are proportional to 1,2,1 and 2,-3,6 is.

Direction cosine : Direction cosine of the line are the cosines of the angles between the line and the three coordinate axis. Direction ratio : Any 3 numbers which Questions » Accounting » Auditing » Find the angle between the lines whose direction Questions Courses. Find the angle between the lines whose direction cosines are given by the equations

The angle between the lines whose direction cosines

The angle between two lines whose direction cosines are l 1 , m 1 , n 1 and l 2 , m 2 , n 2 is —. Last updated on Mar 30, Get Started. SSC Exams. Banking Exams. Teaching Exams. Civil Services Exam. Railways Exams. Engineering Recruitment Exams. Defence Exams. State Govt.

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The angle between two lines whose direction cosines are l 1 , m 1 , n 1 and l 2 , m 2 , n 2 is —. Last updated on Mar 30, Get Started. SSC Exams. Banking Exams. Teaching Exams. Civil Services Exam.

In analytical geometry, the directional cosines also known as direction cosine of a vector is defined as the cosines of the angles between the three coordinate axes and the vector. In this section, we will first learn about the position vector of a point and direction cosines and then finding the angle between two lines. Position vector simply denotes the position or location of a point in the three-dimensional Cartesian system with respect to a reference origin. Taking direction cosines makes it easy to represent the direction of a vector in terms of angles with respect to the reference. The coordinates of the point P may also be expressed as the product of the magnitude of the given vector and the cosines of direction on the three axes, i. Where l, m, n represent the direction cosines of the given vector on the axes x, y, z respectively. We can clearly see that lr, mr, nr are in proportion to the direction cosines and these are called the direction ratios and they are denoted by a, b, c. Let L 1 and L 2 represent two lines having the direction ratios as a 1 , b 1 , c 1, and a 2 , b 2 , c 2 respectively such that they are passing through the origin. Let us choose a random point A on line L 1 and B on line L 2. The direction cosine of the vector can be determined by dividing the corresponding coordinate of a vector by the vector length.

The angle between the lines whose direction cosines

Direction cosine is the cosine of the angle made by the line in the three-dimensional space, with the x-axis, y-axis, z-axis respectively. Direction cosines can be calculated for a vector or a straight line in a three-dimensional space. It is the cosines of the angle made by the line with the three axes. Let us learn more about the direction cosine, the relationship between the direction cosines, and the direction cosine of a line connecting two points in a three-dimensional space.

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