Question
State the vectors which are :
(i) equal in magnitude
(ii) parallel
(iii) in the same direction
(iv) equal
(v) negatives of one another
(i) equal in magnitude
(ii) parallel
(iii) in the same direction
(iv) equal
(v) negatives of one another
✓
Answer
(i) $\bar{a}, \bar{c}$ and $\bar{e} ; \bar{b}$ and $\bar{d}$
(iv) none are equal
(ii) $\bar{a}, \bar{b}, \bar{c}$ and $\bar{d}$
(v) $\bar{a}$ and $\bar{c}, \bar{b}$ and $\bar{d}$
(iii) $\bar{a}$ and $\bar{b} ; \bar{c}$ and $\bar{d}$
(iv) none are equal
(ii) $\bar{a}, \bar{b}, \bar{c}$ and $\bar{d}$
(v) $\bar{a}$ and $\bar{c}, \bar{b}$ and $\bar{d}$
(iii) $\bar{a}$ and $\bar{b} ; \bar{c}$ and $\bar{d}$
Need a full question paper?
Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.
Explore more
Similar questions
In $\triangle A B C$ if $a=13, b=14, c=15$ then find the values of(i) $\cos A$
(ii) $\sin \frac{A}{2}$
(iii) $\cos \frac{A}{2}$
(iv) $\tan \frac{A}{2}$
(v) $A (\triangle ABC )$
(vi) $\sin A$
→(ii) $\sin \frac{A}{2}$
(iii) $\cos \frac{A}{2}$
(iv) $\tan \frac{A}{2}$
(v) $A (\triangle ABC )$
(vi) $\sin A$
Using truth tables, prove the following logical equivalences
i) $(p \wedge q) \equiv \sim(p \rightarrow \sim q)$
ii) $(p \leftrightarrow q) \equiv(p \wedge q) \vee(\sim p \wedge \sim q)$
iii) $(p \wedge q) \rightarrow r \equiv p \rightarrow(q \rightarrow r )$
iv) $p \rightarrow(q \vee r) \equiv(p \rightarrow$ q $) \vee(p \rightarrow r )$
→i) $(p \wedge q) \equiv \sim(p \rightarrow \sim q)$
ii) $(p \leftrightarrow q) \equiv(p \wedge q) \vee(\sim p \wedge \sim q)$
iii) $(p \wedge q) \rightarrow r \equiv p \rightarrow(q \rightarrow r )$
iv) $p \rightarrow(q \vee r) \equiv(p \rightarrow$ q $) \vee(p \rightarrow r )$
Are the following set of vectors linearly independent?
(i) $\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \bar{b}=3 \hat{i}-6 \hat{j}+9 \hat{k}$
(ii) $\bar{a}=-2 \hat{i}-4 \hat{k}, \quad \bar{b}=\hat{i}-2 \hat{j}-\hat{k}, \quad \bar{c}=\hat{i}-4 \hat{j}+3 \hat{k}$. Interpret the results.
→(i) $\bar{a}=\hat{i}-2 \hat{j}+3 \hat{k}, \bar{b}=3 \hat{i}-6 \hat{j}+9 \hat{k}$
(ii) $\bar{a}=-2 \hat{i}-4 \hat{k}, \quad \bar{b}=\hat{i}-2 \hat{j}-\hat{k}, \quad \bar{c}=\hat{i}-4 \hat{j}+3 \hat{k}$. Interpret the results.
In the diagram $\overline{ KL }=\bar{a}, \overline{ LN }=\bar{b}, \overline{ NM }=\bar{c}$ and $\overline{ KT }=\bar{d}$. Find in terms of $\bar{a}, \bar{b}, \bar{c}$ and $\bar{d}$.(i)
(ii) $\overrightarrow{ KM }$
(iii) $\overline{ TN }$
(iv) $\overline{ MT }$
→(ii) $\overrightarrow{ KM }$
(iii) $\overline{ TN }$
(iv) $\overline{ MT }$
Construct the truth table for each of the following statement patterns.
i) $\quad p \rightarrow(q \rightarrow p)$
→i) $\quad p \rightarrow(q \rightarrow p)$
Construct the truth table for each of the following statement patterns.
(ii) (~p ∨ ~q) ↔ [~(p ∧ q)]
(ii) (~p ∨ ~q) ↔ [~(p ∧ q)]
If $A=\{1,2,3,4,5,6,7\}$, determine the truth value of the following.
i) $\exists x \in A$ such that $x-4=3$
ii) $\forall x \in A , \quad x+1 \geq 3$
iii) $\forall x \in A , 8-x \leq 7$
iv) $\exists x \in A$, such that $x+8=16$
→i) $\exists x \in A$ such that $x-4=3$
ii) $\forall x \in A , \quad x+1 \geq 3$
iii) $\forall x \in A , 8-x \leq 7$
iv) $\exists x \in A$, such that $x+8=16$
Find the value of $k$ if $2 x+y=0$ is one of the lines represented by $3 x^2+k x y+2 y^2=0$.
→Reduce the equation $\bar{r} \cdot(3 \hat{i}-4 \hat{j}+12 \hat{k})=8$ to the normal form and hence find
(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.
→(i) the length of the perpendicular from the origin to the plane
(ii) direction cosines of the normal.
If statements p, q are true and r, s are false, determine the truth values of the following. i) i) $\sim p \wedge(q \vee \sim r )$
ii) $(p \wedge \sim r ) \wedge(\sim q \vee s )$
iii) $\sim(p \rightarrow q) \leftrightarrow( r \wedge s )$
iv) $(\sim p \rightarrow q) \wedge( r \leftrightarrow s )$
→ii) $(p \wedge \sim r ) \wedge(\sim q \vee s )$
iii) $\sim(p \rightarrow q) \leftrightarrow( r \wedge s )$
iv) $(\sim p \rightarrow q) \wedge( r \leftrightarrow s )$