The position vectors of $P$ and $Q$ are respectively $\overrightarrow{a}$ and $\overrightarrow{b}$. If $R$ is a point on the line $PQ$ such that $\overrightarrow{PR}=5 \overrightarrow{PQ}$,then the position vector of $R$ is
- A$5 \overrightarrow{b}-4 \overrightarrow{a}$
- B$5 \overrightarrow{b}+4 \overrightarrow{a}$
- C$4 \overrightarrow{b}-5 \overrightarrow{a}$
- D$4 \overrightarrow{b}+5 \overrightarrow{a}$
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Let $u$ and $v$ be non-collinear vectors in $\mathbb{R}^2$. Let $w$ be the orthogonal projection vector of $u$ on $v$. Consider two statements:
$(i)$ Any vector in $\mathbb{R}^2$ can be written as a linear combination of $u$ and $v$.
(ii) $w$ can be written as a linear combination of $u$ and $v$ as $w = au + bv$,where both $a$ and $b$ are non-zero real numbers.
$(i)$ Any vector in $\mathbb{R}^2$ can be written as a linear combination of $u$ and $v$.
(ii) $w$ can be written as a linear combination of $u$ and $v$ as $w = au + bv$,where both $a$ and $b$ are non-zero real numbers.
If $|\overline{u}|=2$ and $\overline{u}$ makes angles of $60^{\circ}$ and $120^{\circ}$ with axes $OX$ and $OY$ respectively,then $\overline{u}=$
Classify the following as scalar and vector quantities:
Force
Force
Easy
View SolutionIf $\theta$ is the interior angle of a regular pentagon,then $|(\sin \theta) \hat{i}+(\cos \theta) \hat{j}+(\tan \theta) \hat{k}|=$
State whether the following statement is true or false:
Two vectors having the same magnitude are collinear.
Two vectors having the same magnitude are collinear.
Medium
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