Question

Find the direction cosine of the following vectors.
A. 3i-9j+2k b.) i+7j-5k (c.) 4i+3j-11k( d.) 10i-j+2k

Answer 1

(a) a=3i-9j+2k

$\mid a\mid=\sqrt{3^2+9^2+2^2}\approx9.7$

$\cos\alpha=3/9.7=0.309$

$\cos\beta=-9/9.7=-0.928$

$\cos\gamma=2/9.7=0.206$

(b) a=i+7j-5k

$\mid a\mid=\sqrt{1^2+7^2+5^2}\approx8.66$

$\cos\alpha=1/8.66=0.115$

$\cos\beta=7/8.66=0.808$

$\cos\gamma=-5/8.66=0.577$

(c) a=4i+3j-11k

$\mid a\mid=\sqrt{4^2+3^2+11^2}\approx12.1$

$\cos\alpha=4/12.1=0.331$

$\cos\beta=3/12.1=0.248$

$\cos\gamma=-11/12.1=-0.909$

(d) a=10i-j+2k

$\mid a\mid=\sqrt{10^2+1^2+2^2}\approx10.25$

$\cos\alpha=10/10.25=0.976$

$\cos\beta=-1/10.25=-0.098$

$\cos\gamma=2/10.25=0.195$