Ncert Solutions Maths class 12th

Two different vectors having same magnitude: -

(i) $2\hat{i}+\hat{j}+3\hat{k}$

(ii) $\hat{i}+3\hat{j}+2\hat{k}$

Kindly go through the solution

(i) True, as vector quantity $\overrightarrow{a}$ and - $\overrightarrow{a}$ are parallel to same line.

(ii) False, as collinear vector are those vectors that are parallel to same line, but it is not necessary that they are equal also.

(iii) False, as two vectors having same magnitude may have different direction

(a) Vector $\overrightarrow{a}$ and $\overrightarrow{d}$ are co initial same initial point.

(b) $\overrightarrow{b}$ and $\stackrel{?}{d}$ same magnitude & direction.

(c) $\overrightarrow{a}$ and $\overrightarrow{c}$ are collinear but not equal they are parallels their direction are not same.

95.

$\begin{array}{l}P\left(A\right)+P\left(B\right)-P\left(AandB\right)=P\left(A\right)\\ \Rightarrow P\left(A\right)+P\left(B\right)-P\left(A\cap B\right)=P\left(A\right)\\ \Rightarrow P\left(B\right)-P\left(A\cap B\right)=0\\ \Rightarrow P\left(A\cap B\right)=P\left(B\right)\\ \therefore P\left(A|B\right)=\frac{P\left(A\cap B\right)}{P\left(B\right)}=\frac{P\left(B\right)}{P\left(B\right)}=1\end{array}$

Therefore, option (B) is correct.

(i) Time period involves only magnitude. So, it is scalar quantity.

(ii) Distance involves only magnitude. So, it is scalar quantity.

(iii) Force involves both magnitude and direction. So, it is vector quantity.

(iv) Velocity involves both magnitude and direction. So, it is vector quantity.

(v) Wor

(i) 10kg involves only magnitude. So, it is scalar quantity.

(ii) 2 meters north-west involves both magnitude and direction. So, it is vector quantity.

(iii) 40⁰  involves only magnitude. So, it is scalar quantity.

(iv) 40⁰  watts involves only magnitude. So, it is scalar quantity.

(v)

94.

$\begin{array}{l}P\left(A|B\right)>P\left(A\right)\\ \Rightarrow \frac{P\left(A\cap B\right)}{P\left(B\right)}>P\left(A\right)\\ \Rightarrow P\left(A\cap B\right)>P\left(A\right).P\left(B\right)\\ \Rightarrow \frac{P\left(A\cap B\right)}{P\left(A\right)}>P\left(B\right)\\ \Rightarrow P\left(B|A\right)>P\left(B\right)\end{array}$

Therefore, option (C) is correct.

$40km,30^0$ east of north.