**Tutorial Exercise**Consider the two vectors \( \vec{A} = 2 \hat{\imath} - 2 \hat{\jmath} \) and \( \vec{B} = - \hat{\imath} - 5 \hat{\jmath} \).(a) Calculate \( \vec{A} + \vec{B} \)(b) Calculate \( \vec{A} - \vec{B} \)(c) Calculate \( |\vec{A} + \vec{B}| \)(d) Calculate \( |\vec{A} - \vec{B}| \)(e) Calculate the directions of \( \vec{A} + \vec{B} \) and \( \vec{A} - \vec{B} \).**Step 1**You can draw the vectors \( \vec{A} \) and \( \vec{B} \) on graph paper in the x-y plane. The vector \( \vec{A} \) is drawn from the origin to the point (2, -2), and the vector \( \vec{B} \) is drawn from the origin to the point (-1, -5).**Step 2**We perform operations on vectors in unit-vector form by performing the operations on the coefficients of the unit vectors \( \hat{\imath} \) and \( \hat{\jmath} \). Part (a) asks for the addition of two vectors. Part (b) asks for the difference of two vectors, and parts (c) and (d) ask for the magnitudes of the two resulting vectors from parts (a) and (b). Part (e) asks for the directions of the two vectors from parts (a) and (b).**Step 3**(a) Use the property of vector addition that states that the components of \( \vec{R} = \vec{A} + \vec{B} \) are computed as \( R_x = A_x + B_x \) and \( R_y = A_y + B_y \).\[ \vec{A} + \vec{B} = (2 \hat{\imath} + (-2) \hat{\jmath}) + (- \hat{\imath} + (-5) \hat{\jmath}) = \hat{\imath} + \hat{\jmath} \]

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Answered: Consider the two vectors A = 2 1 - 2 ĵ…

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Physics

Consider the two vectors A = 2 1 - 2 ĵ and B = - î - 5₁. (a) Calculate A + B (b) Calculate A - B A+B (c) Calculate

College Physics

11th Edition

ISBN:9781305952300

Author:Raymond A. Serway, Chris Vuille

Publisher:Raymond A. Serway, Chris Vuille

Chapter1: Units, Trigonometry. And Vectors

Section: Chapter Questions

Problem 1CQ: Estimate the order of magnitude of the length, in meters, of each of the following; (a) a mouse, (b)...

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Scalars and Vectors

Scalars and Vectors are the classification of physical quantities that are used to denote various terms in physics.

Question

**Tutorial Exercise**

Consider the two vectors \( \vec{A} = 2 \hat{\imath} - 2 \hat{\jmath} \) and \( \vec{B} = - \hat{\imath} - 5 \hat{\jmath} \).

(a) Calculate \( \vec{A} + \vec{B} \)

(b) Calculate \( \vec{A} - \vec{B} \)

(c) Calculate \( |\vec{A} + \vec{B}| \)

(d) Calculate \( |\vec{A} - \vec{B}| \)

(e) Calculate the directions of \( \vec{A} + \vec{B} \) and \( \vec{A} - \vec{B} \).

**Step 1**

You can draw the vectors \( \vec{A} \) and \( \vec{B} \) on graph paper in the x-y plane. The vector \( \vec{A} \) is drawn from the origin to the point (2, -2), and the vector \( \vec{B} \) is drawn from the origin to the point (-1, -5).

**Step 2**

We perform operations on vectors in unit-vector form by performing the operations on the coefficients of the unit vectors \( \hat{\imath} \) and \( \hat{\jmath} \). Part (a) asks for the addition of two vectors. Part (b) asks for the difference of two vectors, and parts (c) and (d) ask for the magnitudes of the two resulting vectors from parts (a) and (b). Part (e) asks for the directions of the two vectors from parts (a) and (b).

**Step 3**

(a) Use the property of vector addition that states that the components of \( \vec{R} = \vec{A} + \vec{B} \) are computed as \( R_x = A_x + B_x \) and \( R_y = A_y + B_y \).

\[
\vec{A} + \vec{B} = (2 \hat{\imath} + (-2) \hat{\jmath}) + (- \hat{\imath} + (-5) \hat{\jmath})
= \hat{\imath} + \hat{\jmath}
\]

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