Question
$\text{If}\ \ \vec{\text{a}}=\vec{\text{b}}+\vec{\text{c}},$ then is it true that $\big|\vec{\text{a}}\big|=\big|\vec{\text{b}}\big|+\big|\vec{\text{c}}\big|?$ Justify your answer.
✓
Answer
$\text{If}\ \triangle\text{ABC},\ \text{let}\ \overrightarrow{\text{CB}}=\vec{\text{a}},\ \overrightarrow{\text{CA}}=\vec{\text{b}},\text{and}\ \overrightarrow{\text{AB}}=\vec{\text{c}}$ (as shown in the following figure).
Now, by the triangle law of vector additio, we have $\vec{\text{a}}=\vec{\text{b}}+\vec{\text{c}}$It is clearly known that $|\vec{\text{a}}|,\big|\vec{\text{b}}\big|,\ \text{and}\ \big|\vec{\text{c}}\big|$ represent the sides of $\triangle\text{ABC}.$
Also, it is known that the sum of the lengths of any two sides of a triangle is greater than the third side. $\therefore\ |\vec{\text{a}}|<\big|\vec{b}\big|+|\vec{c}|$ Hence, it is not true that $|\vec{\text{a}}|=\big|\vec{\text{b}}\big|+\big|\vec{\text{c}}\big|$
Now, by the triangle law of vector additio, we have $\vec{\text{a}}=\vec{\text{b}}+\vec{\text{c}}$It is clearly known that $|\vec{\text{a}}|,\big|\vec{\text{b}}\big|,\ \text{and}\ \big|\vec{\text{c}}\big|$ represent the sides of $\triangle\text{ABC}.$
Also, it is known that the sum of the lengths of any two sides of a triangle is greater than the third side. $\therefore\ |\vec{\text{a}}|<\big|\vec{b}\big|+|\vec{c}|$ Hence, it is not true that $|\vec{\text{a}}|=\big|\vec{\text{b}}\big|+\big|\vec{\text{c}}\big|$
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
$\int\frac{1}{2-3\text{x}}+\frac{1}{\sqrt{3\text{x}-2}}\text{dx}$
→Give examples of two functions f : N → N and g : N → N, such that gof is onto but f is not onto.
Represent the following families of curves by forming the corresponding differential equation:
$\text{x}^2+(\text{y}-\text{b})^2=1$
→$\text{x}^2+(\text{y}-\text{b})^2=1$
Discuss the applicability of the Rolle's theorem for the following function on the indicated interval
$\text{f}(\text{x})=3+(\text{x}-2)^{\frac{2}{3}}\text{ on }[1,3]$
→$\text{f}(\text{x})=3+(\text{x}-2)^{\frac{2}{3}}\text{ on }[1,3]$
A coin is tossed 5 times. What is the probability that head appears an even number of times?
Solve the following equation for x:
$\tan^{-1}\frac{\text{x}-2}{\text{x}-1}+\tan^{-1}\frac{\text{x}+2}{\text{x}+1}=\frac{\pi}{4}$
→$\tan^{-1}\frac{\text{x}-2}{\text{x}-1}+\tan^{-1}\frac{\text{x}+2}{\text{x}+1}=\frac{\pi}{4}$
For what value of k is the following function continuous at x = 1
$\text{f}\text{(x)}=\begin{cases}\frac{\text{x}^2-1}{\text{x}-1}, & \text{x} \neq 1\\\text{k}, & \text{x}= 1\end{cases}$
→$\text{f}\text{(x)}=\begin{cases}\frac{\text{x}^2-1}{\text{x}-1}, & \text{x} \neq 1\\\text{k}, & \text{x}= 1\end{cases}$
Solve the following differential equation $\frac{d y}{d x}=1+x^2+y^2+x^2 y^2$, given that $y =1$, when $x =0$.
→A bag contains 8 red and 6 green balls. Three balls are drawn one after another without replacement. Find the probability that at least two balls drawn are green.
Integrate the function $\sqrt{1-4 x-x^{2}}$
→