Question

Please don't post irrelevant answers.
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Answer 1

6. The given vectors can be represented in vector form as,

$\longrightarrow\vec{\sf{A}}=\sf{15(\cos127^o\ \hat i+\sin127^o\ \hat j)}$

$\longrightarrow\vec{\sf{A}}=\sf{15\left(-\dfrac{3}{5}\ \hat i+\dfrac{4}{5}\ \hat j\right)}$

$\longrightarrow\vec{\sf{A}}=\sf{-9\ \hat i+12\ \hat j}$

and,

$\longrightarrow\vec{\sf{B}}=\sf{10(\cos53^o\ \hat i+\sin53^o\ \hat j)}$

$\longrightarrow\vec{\sf{B}}=\sf{10\left(\dfrac{3}{5}\ \hat i+\dfrac{4}{5}\ \hat j\right)}$

$\longrightarrow\vec{\sf{B}}=\sf{6\ \hat i+8\ \hat j}$

Hence their resultant will be,

$\longrightarrow\vec{\sf{R}}=\vec{\sf{A}}+\vec{\sf{B}}$

$\longrightarrow\vec{\sf{R}}=\sf{-9\ \hat i+12\ \hat j+6\ \hat i+8\ \hat j}$

$\longrightarrow\vec{\sf{R}}=\sf{(-9+6)\ \hat i+(12+8)\ \hat j}$

$\longrightarrow\vec{\sf{R}}=\sf{-3\ \hat i+20\ \hat j}$

whose magnitude will be,

$\sf{\longrightarrow R=\sqrt{(-3)^2+20^2}}$

$\sf{\longrightarrow R=\sqrt{9+400}}$

$\sf{\longrightarrow R=\sqrt{409}}$

$\sf{\longrightarrow\underline{\underline{R=20.19}}}$

Hence (a) is the answer.

7. The vectors can be represented in vector form as,

$\longrightarrow\vec{\sf{A}}=\sf{5\ \hat i}$

and,

$\longrightarrow \vec{\sf{B}}=\sf{5(\cos37^o\ \hat i+\sin 37^o\ \hat j)}$

$\longrightarrow \vec{\sf{B}}=\sf{5\left(\dfrac{4}{5}\ \hat i+\dfrac{3}{5}\ \hat j\right)}$

$\longrightarrow \vec{\sf{B}}=\sf{4\ \hat i+3\ \hat j}$

and,

$\longrightarrow\vec{\sf{C}}=\sf{5(\cos53^o\ \hat i+\sin53^o\ \hat j)}$

$\longrightarrow\vec{\sf{C}}=\sf{5\left(\dfrac{3}{5}\ \hat i+\dfrac{4}{5}\ \hat j\right)}$

$\longrightarrow\vec{\sf{C}}=\sf{3\ \hat i+4\ \hat j}$

Hence their resultant will be,

$\longrightarrow \vec{\sf{R}}=\vec{\sf{A}}+\vec{\sf{B}}+\vec{\sf{C}}$

$\longrightarrow\vec{\sf{R}}=\sf{5\ \hat i+4\ \hat i+3\ \hat j+3\ \hat i+4\ \hat j}$

$\longrightarrow\vec{\sf{R}}=\sf{(5+4+3)\hat i+(3+4)\ \hat j}$

$\longrightarrow\vec{\sf{R}}=\sf{12\ \hat i+7\ \hat j}$

whose magnitude will be,

$\sf{\longrightarrow R=\sqrt{12^2+7^2}}$

$\sf{\longrightarrow R=\sqrt{144+49}}$

$\sf{\longrightarrow R=\sqrt{193}}$

$\sf{\longrightarrow\underline{\underline{R=13.89}}}$

Hence (c) is the answer.