Question

(10 pts) Here are three displacements, each measured in meters: \(\vec{d_1} = 4.0\hat{i} + 5.0\hat{j} - 6.0\hat{k}\), \(\vec{d_2} = -1.0\hat{i} + 2.0\hat{j} + 3.0\hat{k}\) and \(\vec{d_3} = 4.0\hat{i} + 3.0\hat{j} + 2.0\hat{k}\). a) If \(\vec{r} = \vec{d_1} - \vec{d_2} + \vec{d_3}\), What is the angle between \(\vec{r}\) and the positive \(\hat{j}\) axis? b) What is the component of \(\vec{d_2}\) along the direction of \(\vec{d_3}\)

          (10 pts) Here are three displacements, each measured in meters: \(\vec{d_1} = 4.0\hat{i} + 5.0\hat{j} - 6.0\hat{k}\), \(\vec{d_2} = -1.0\hat{i} + 2.0\hat{j} + 3.0\hat{k}\) and \(\vec{d_3} = 4.0\hat{i} + 3.0\hat{j} + 2.0\hat{k}\).
 a) If \(\vec{r} = \vec{d_1} - \vec{d_2} + \vec{d_3}\), What is the angle between \(\vec{r}\) and the positive \(\hat{j}\) axis?
b) What is the component of \(\vec{d_2}\) along the direction of \(\vec{d_3}\)

(10 pts) Here are three displacements, each measured in meters: d⃗1⃗ = 4.0î + 5.0ĵ - 6.0k̂, d⃗2⃗ = -1.0î + 2.0ĵ + 3.0k̂ and d⃗3⃗ = 4.0î + 3.0ĵ + 2.0k̂.
a) If r⃗ = d⃗1⃗ - d⃗2⃗ + d⃗3⃗, What is the angle between r⃗ and the positive ĵ axis?
b) What is the component of d⃗2⃗ along the direction of d⃗3⃗

Added by Daniel R.

University Physics with Modern Physics

Hugh D. Young 14th Edition

Instant Answer

Solved by Expert Sri K

06/16/2022

Step 1

To calculate the vector r, we need to subtract d2 from d, and then add d3 to the result. r = d - d2 + d3 = (4.0i + 5.0j - 6.0k) - (-1.0i + 2.07j + 3.0k) + (4.0i + 3.0j + 2.0k) = 4.0i + 5.0j - 6.0k + 1.0i - 2.07j - 3.0k + 4.0i + 3.0j + 2.0k = (4.0i + 1.0i + Show more…

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Here are three displacements, each measured in meters: d = 4.0i + 5.0j - 6.0k, d2 = -1.0i + 2.07j + 3.0k, and d3 = 4.0i + 3.0j + 2.0k. a) If r = d - d2 + d3, what is the angle between r and the positive axis? b) What is the component of d along the direction of d3?