Find the direction cosines of the vector v

Assignment Help Mathematics

Reference no: EM131010564

As shown in the figure, the direction cosines represent the cosines of the angles made between the vector and the three coordinate directions.

958_The direction cosines.jpg

The direction cosines of a nonzero vector v = A_Xi + A_Yj + A_Zk

cos α = A_X/||v||
cos β = A_Y/||v||
cos γ= A_Z/||v||

where the angles α, β, and γ are the angles shown in the figure.

a. Show that: cos² α + cos² β + cos² γ = 1.

b. Find the direction cosines of the vector v = 2i - 4j + 4k. and approximate the direction angle to the nearest degree.

Reference no: EM131010564

Questions Cloud

Do you think this is an effective use of a pie chart : Do you think this is an effective use of a pie chart? Why or why not? Construct a bar chart to show the distribution of deaths by object struck. Is this display more effective than the pie chart in summarizing this data set? Explain.

Define the measurement system : Define the measurement system (BSC) to evaluate the achievement of strategic objectives. Define the organigram of your Company (or the intended evolution of the existing one)

Determine the effect of the errors on retained earnings at : In 2016, Winslow International, Inc.'s controller discovered that ending inventories for 2014 and 2015 were overstated by 5,380,000 and 5680.000, respectively. Determine the effect of the errors on retained earnings at January 1, 2016.

Effective leaders both learn from the past : Effective leaders both learn from the past and are able to adapt what they have learned to the present context. In your paper, discuss how you, as a leader or potential leader in a professional or community context, can challenge the status quo and m..

Find the direction cosines of the vector v : Show that: cos2 α + cos2 β + cos2 γ = 1. Find the direction cosines of the vector v = 2i - 4j + 4k. and approximate the direction angle to the nearest degree.

Identify the expected performance of the group : Identify the expected performance of the group or individuals as a result of the training

What is the difference between philosophy and science : What is the difference between philosophy and science? In answering this question, be sure to include the difference between Epistemology and Methodology; and the various errors of social inquiry and possible solutions.

Consider the spot interest rates for maturities : Consider the following spot interest rates for maturities of one, two, three, and four years. r1 = 4.6% r2 = 5.2% r3 = 5.9% r4 = 6.7% Assuming a constant real interest rate of 2 percent, what are the approximate expected inflation rates for the next ..

What is the present value of the annuity : What is the present value of the following annuity? $3346 every half year at the end of the period for the next 15 years, discounted back to the present at 19.78 percent, per year, compounded SEMIANNUALLY.

User Account

All Pages