Find angle between vec A = 3hat{i} - hat{j} + 4hat{k} and Z- axis

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3-1.Vectors

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Find angle between $\vec A = 3\hat i - \hat j + 4\hat k$ and $Z-$ axis

${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {22} }}{4}} \right)$

${\tan ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$

${\sin ^{ - 1}}\,\left( {\frac{{\sqrt {10} }}{4}} \right)$

${\sin ^{ - 1}}\,\left( {\frac{4}{{\sqrt {26} }}} \right)$

Solution

$\cos \theta=\frac{\overrightarrow{\mathrm{A}} \cdot \overrightarrow{\mathrm{B}}}{\mathrm{AB}}=\frac{(3 \hat{\mathrm{i}}-\hat{j}+4 \hat{\mathrm{k}}) \cdot(\hat{\mathrm{k}})}{\sqrt{(3)^{2}+(-1)^{2}+(4)^{2}} \sqrt{(1)^{2}}}=\frac{4}{\sqrt{26}}$

Base $=4,$ hypotenuse $=\sqrt{26} \cdot$ perpendicular $=\sqrt{10}$

$\tan \theta=\frac{\sqrt{10}}{4}, \quad \theta=\tan ^{-1}\left(\frac{\sqrt{10}}{4}\right)$

Standard 11

Physics

If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $……m$.

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(JEE MAIN-2022)

The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ……. $^o$

medium

Three particles ${P}, {Q}$ and ${R}$ are moving along the vectors $\vec{A}=\hat{{i}}+\hat{{j}}, \vec{B}=\hat{{j}}+\hat{{k}}$ and $\vec{C}=-\hat{{i}}+\hat{{j}}$ respectively. They strike on a point and start to move in different directions. Now particle $P$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{B} .$ Similarly particle $Q$ is moving normal to the plane which contains vector $\vec{A}$ and $\vec{C} .$ The angle between the direction of motion of $P$ and $Q$ is $\cos ^{-1}\left(\frac{1}{\sqrt{x}}\right)$. Then the value of $x$ is …… .

hard

(JEE MAIN-2021)

If a vector $\vec A$ is parallel to another vector $\vec B$ then the resultant of the vector $\vec A \times \vec B$ will be equal to

medium

For component of a vector $A =(3 \hat{ i }+4 \hat{ j }-5 \hat{ k })$, match the following colum.

Colum $I$ Colum $II$

$(A)$ $x-$axis $(p)$ $5\,unit$

$(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$ $(q)$ $4\,unit$

$(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$ $(r)$ $0$

$(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ $(s)$ None

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Colum $I$	Colum $II$
$(A)$ $x-$axis	$(p)$ $5\,unit$
$(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$	$(q)$ $4\,unit$
$(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$	$(r)$ $0$
$(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$	$(s)$ None

Find angle between $\vec A = 3\hat i - \hat j + 4\hat k$ and $Z-$ axis

Solution

Similar Questions

If $\overrightarrow{ A }=(2 \hat{ i }+3 \hat{ j }-\hat{ k }) \;m$ and $\overrightarrow{ B }=(\hat{ i }+2 \hat{ j }+2 \hat{ k })\; m$. The magnitude of component of vector $\overrightarrow{ A }$ along vector $\vec{B}$ will be $……m$.

The angle between two vectors $4\hat i + 3\hat j + \hat k$ and $-3\hat i + 2\hat j + 6\hat k$ is ……. $^o$

If a vector $\vec A$ is parallel to another vector $\vec B$ then the resultant of the vector $\vec A \times \vec B$ will be equal to

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