A vector r vector has magnitude 14 and direction ratios 2,3,-6 Find the directino cosines and components of r - Maths - Vector Algebra

Question

A vector r vector has magnitude 14 and direction ratios 2,3,-6
Find the directino cosines and components of r vector ,given that r
vector makes an acute angle with x-axis

Priyanka Kedia · Accepted Answer

Given, a vector r→ has magnitude 14 and direction ratios are 2,3,-6
 So, r→=14Let l,m,n are the direction cosines of r→
 Since r→ makes an acute angle with x-axis, so,  l>0Direction ratios of  are 2,3,-6, so,Direction cosinesl,m,n of r→=222+32+-62,322+32+-62,-622+32+-62                                                =249,349,-649                                                =27,37,-67Thus,Direction cosines of r→are l=27,m=37, and n=-67Also,r→=r→li⏜+mj⏜+nk⏜=1427i⏜+37j⏜-67k⏜=4i⏜+6j⏜-12k⏜Hence, components of r→ along x-axis, y-axis and z-axis are 4i⏜,6j⏜, and -12k⏜ respectively

A vector r vector has magnitude 14 and direction ratios 2,3,-6 .Find the directino cosines and components of r vector ,given that r vector makes an acute angle with x-axis.