For any two vectors vec{a} and vec{b},which o | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) According to the triangle inequality for vectors,for any two vectors $\vec{a}$ and $\vec{b}$,the magnitude of their sum is always less than or equ

Vedclass · Accepted Answer

$|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$

Vedclass · Answer

(A) According to the triangle inequality for vectors,for any two vectors $\vec{a}$ and $\vec{b}$,the magnitude of their sum is always less than or equal to the sum of their magnitudes,i.e.,$|\vec{a} + \vec{b}| \le |\vec{a}| + |\vec{b}|$.Also,the reverse triangle inequality states that $|\vec{a} + \vec{b}| \ge ||\vec{a}| - |\vec{b}||$.Since $|\vec{a}| - |\vec{b}| \le ||\vec{a}| - |\vec{b}||$,it follows that $|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$.Therefore,the statement $|\vec{a} + \vec{b}| \ge |\vec{a}| - |\vec{b}|$ is always true.

For any two vectors $\vec{a}$ and $\vec{b}$,which of the following statements is true?

Similar Questions

If $\vec{a}, \vec{b}, \vec{c}$ are unit vectors,then what is the maximum value of $|\vec{a} - \vec{b}|^2 + |\vec{b} - \vec{c}|^2 + |\vec{c} - \vec{a}|^2$?

Classify the following measure as a scalar or a vector:
$40^{o}$

If $G$ is the centroid of the $\triangle ABC$,then $\vec{GA} + \vec{GB} + \vec{GC}$ is equal to

If $a$ and $b$ are two vectors such that $a \cdot b = 0$ and $a \times b = 0$,then:

$A$ vector of magnitude $\sqrt{2}$ units along the internal bisector of the angle between the vectors $\vec{a} = 2 \hat{i} - 2 \hat{j} + \hat{k}$ and $\vec{b} = \hat{i} + 2 \hat{j} + 2 \hat{k}$ is

Vedclass Test Series

Exam Paper Generator

Online Exam Module