11판/3. 벡터 44

3-44 할리데이 11판 솔루션 일반물리학

{r=(5.25i^+4.90j^+3.00k^)[m] \begin{cases} \vec r &= \(5.25\i+4.90\j+3.00\k\)\ut{m} \end{cases} (a)\ab{a} r=5.252+4.92+32=12024229[m]7.782833674183202[m]7.78[m] \begin{aligned} r &= \sqrt{5.25^2+4.9^2+3^2}\\ &=\frac{1}{20}\sqrt{24229}\ut{m}\\ &\approx 7.782833674183202\ut{m}\\ &\approx 7.78\ut{m}\\ \end{aligned} (b)\ab{b} l<r ?l\lt r ~? [Impossible]\title{Impossible} (c)\ab{c} l>r ?l\gt r ~? [Possible]\title{Possible} (d)\ab{d} l=r ?l = r ~? [Possible]\title{Possible} (e)\ab{e} $$\ve..

11판/3. 벡터 2024.01.25

3-43 할리데이 11판 솔루션 일반물리학

{A=7.00[km]j^B=10.5[km]θB=60° \begin{cases} \vec A &= 7.00\ut{km}\j\\ B&=10.5\ut{km}\\ \theta_B&=60\degree\\ \end{cases} B=10.5cos60°i^+10.5sin60°j^=214i^+2143j^ \begin{aligned} \vec B &=10.5\cos60\degree\i+10.5\sin60\degree\j\\ &=\frac{21}{4}\i+\frac{21}{4}\sqrt{3}\j \end{aligned} C=B+A=(214i^+2143j^)+7j^=214i^+(72143)j^ \begin{aligned} \vec C &=-\vec B+\vec A\\ &=-\(\frac{21}{4}\i+\frac{21}{4}\sqrt{3}\j\)+7\j\\ &=-\frac{21}{4}\i+\(7-\frac{21}{4}\sqrt{3}\)\j\\ \end{aligned} (a)\ab{a} $..

11판/3. 벡터 2024.01.25

3-42 할리데이 11판 솔루션 일반물리학

{d=1.5[m]j^ \begin{cases} \vec d &=-1.5\ut{m}\j \end{cases} (a)\ab{a} 6.0d=9j^=9 \begin{aligned} \abs{6.0\vec d} &= \abs{-9\j}\\ &=9 \end{aligned} (b)\ab{b} South\text{South} (c)\ab{c} 2.0d=3j^=3 \begin{aligned} \abs{-2.0\vec d} &= \abs{3\j}\\ &=3 \end{aligned} (b)\ab{b} North\text{North}

11판/3. 벡터 2024.01.25

3-41 할리데이 11판 솔루션 일반물리학

{a=6.0i^+5.0j^b=3.0i^+4.0j^ \begin{cases} \vec a&=6.0\i+5.0\j\\ \vec b&=3.0\i+4.0\j\\ \end{cases} (a)\ab{a} a×b=(aybzbyaz)i^+(azbxbzax)j^+(axbybxay)k^, \vec a\times \vec b=(a_yb_z-b_ya_z)\i+(a_zb_x-b_za_x)\j+(a_xb_y-b_xa_y)\k, a×b=(6i^+5j^)×(3i^+4j^)=(6×45×3)k^=9k^ \begin{aligned} \vec a \times \vec b &=\(6\i+5\j\)\times\(3\i+4\j\)\\ &=(6\times4-5\times3)\k\\ &=9\k \end{aligned} (b)\ab{b} ab=axbx+ayby+azbz,\vec a \cdot \vec b=a_xb_x+a_yb_y+a_zb_z, $$ \begin{aligned} \vec a \cdot \vec b&=\(6\i+5\j\)..

11판/3. 벡터 2024.01.25

3-40 할리데이 11판 솔루션 일반물리학

{East:+i^North:+j^up:+k^ \begin{cases} \text{East}:+\i\\ \text{North}:+\j\\ \text{up}:+\k\\ \end{cases} (a)\ab{a} Ans=(j^)×(i^)=(1)(1)(j^×i^)=(j^×i^)=(1)(i^×j^)=(1)(k^)=k^Down \begin{aligned} \Ans&=\(-\j\)\times\(-\i\)\\ &=(-1)(-1)\(\j\times\i\)\\ &=\(\j\times\i\)\\ &=(-1)\(\i\times\j\)\\ &=(-1)\(\k\)\\ &=-\k\\ &\text{Down} \end{aligned} (b)\ab{b} $$ \begin{aligned} \Ans&=\(-\k\)\times\(-\j\)\\ &=(-1)(-1)\(\k\times\j\)\\ &=\(\k\times\j\)\\ &=(-1)\(\j\times\k\)\\ &=(-..

11판/3. 벡터 2024.01.25

3-38 할리데이 11판 솔루션 일반물리학

{d1=(2.0i^+3.0j^+4.0k^)[m]d2=(2.0i^4.0j^+3.0k^)[m]d3=(2.0i^+3.0j^+2.5k^)[m] \begin{cases} \vec d_1 &= \(-2.0\i+3.0\j+4.0\k\)\ut{m}\\ \vec d_2 &= \(-2.0\i-4.0\j+3.0\k\)\ut{m}\\ \vec d_3 &= \(2.0\i+3.0\j+2.5\k\)\ut{m}\\ \end{cases} (a)\ab{a} ab=axbx+ayby+azbz,\vec a \cdot \vec b=a_xb_x+a_yb_y+a_zb_z, $$ \begin{aligned} \Ans&=\vec d_1\cdot\(\vec d_2+\vec d_3\)\\ &=\vec d_1\cdot\bra{\(-2\i-4\j+3\k\)+\(2\i+3\j+2.5\k\)}\\ &=\(-2\i+3\j+4\k\)\cdot\(-\j+5.5\k\)\\ &=(-2)\cdot0+3\cdot(-1..

11판/3. 벡터 2024.01.25

3-37 할리데이 11판 솔루션 일반물리학

{a=8i^b=6j^c=8i^6j^ \begin{cases} \vec a &= 8\i\\ \vec b &= 6\j\\ \vec c &= -8\i-6\j\\ \end{cases} (a)\ab{a} ab=80+06=0 \begin{aligned} \vec a\cdot\vec b&=8\cdot0+0\cdot6\\ &=0 \end{aligned} (b)\ab{b} ac=8(8)+0(6)=64 \begin{aligned} \vec a\cdot\vec c&=8\cdot(-8)+0\cdot(-6)\\ &=-64 \end{aligned} (c)\ab{c} bc=0(8)+6(6)=36 \begin{aligned} \vec b\cdot\vec c&=0\cdot(-8)+6\cdot(-6)\\ &=-36 \end{aligned}

11판/3. 벡터 2024.01.25

3-36 할리데이 11판 솔루션 일반물리학

{A=0B=55[km]i^r1=24[km],θ1=25°r2=8.0[km]j^ \begin{cases} \vec A &= 0\\ \vec B &= 55\ut{km}\i\\ r_1&=24\ut{km}, \theta_1=-25\degree\\ \vec r_2 &= 8.0\ut{km}\j \end{cases} C=(A+r1+r2)B=(0+24cos(25°)i^+24sin(25°)+8j^)55i^=(24cos25°55)i^+(824sin25°)j^ \begin{aligned} \vec C &= \(\vec A + \vec r_1 + \vec r_2\)-\vec B\\ &=\(0 + 24\cos(-25\degree)\i+24\sin(-25\degree) + 8\j\)-55\i\\ &=(24\cos25\degree-55)\i+(8-24\sin25\degree)\j\\ \end{aligned} $$ \begin{aligned} C &= \sqrt{(24\cos25\degree-55)^2+(8-24\sin25\..

11판/3. 벡터 2024.01.25

3-35 할리데이 11판 솔루션 일반물리학

{a=ai^b=bj^d>0 \begin{cases} \vec a &= a\i\\ \vec b &= -b\j\\ d&>0 \end{cases} (a)\ab{a} bd=bj^d=bdj^ \begin{aligned} \frac{\vec b}{d}&=\frac{-b\j}{d}\\ &=-\frac{b}{d}\j\\ \end{aligned} bd<0-\frac{b}{d}\lt0 y\therefore -y (b)\ab{b} bd=bj^d=bdj^ \begin{aligned} \frac{\vec b}{-d}&=\frac{-b\j}{-d}\\ &=\frac{b}{d}\j\\ \end{aligned} bd>0\frac{b}{d}\gt0 +y\therefore +y (c)\ab{c} $$ \begin{aligned} \vec a \cdot \vec ..

11판/3. 벡터 2024.01.24