If the lengths of three vectors bar{a}, bar{b | vedclass

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

Question

(A) Given that $|\bar{a}| = 5$,$|\bar{b}| = 12$,and $|\bar{c}| = 13$. Since each vector is perpendicular to the sum of the other two,we have: $\bar{a}

Vedclass · Accepted Answer

$\sqrt{338}$

Vedclass · Answer

(A) Given that $|\bar{a}| = 5$,$|\bar{b}| = 12$,and $|\bar{c}| = 13$. Since each vector is perpendicular to the sum of the other two,we have: $\bar{a} \cdot (\bar{b} + \bar{c}) = 0 \implies \bar{a} \cdot \bar{b} + \bar{a} \cdot \bar{c} = 0$ $\bar{b} \cdot (\bar{a} + \bar{c}) = 0 \implies \bar{b} \cdot \bar{a} + \bar{b} \cdot \bar{c} = 0$ $\bar{c} \cdot (\bar{a} + \bar{b}) = 0 \implies \bar{c} \cdot \bar{a} + \bar{c} \cdot \bar{b} = 0$ From these equations,it follows that $\bar{a} \cdot \bar{b} = 0$,$\bar{b} \cdot \bar{c} = 0$,and $\bar{c} \cdot \bar{a} = 0$. Now,consider the magnitude squared: $|\bar{a} + \bar{b} + \bar{c}|^2 = |\bar{a}|^2 + |\bar{b}|^2 + |\bar{c}|^2 + 2(\bar{a} \cdot \bar{b} + \bar{b} \cdot \bar{c} + \bar{c} \cdot \bar{a})$ $|\bar{a} + \bar{b} + \bar{c}|^2 = 5^2 + 12^2 + 13^2 + 2(0 + 0 + 0)$ $|\bar{a} + \bar{b} + \bar{c}|^2 = 25 + 144 + 169 = 338$ Therefore,$|\bar{a} + \bar{b} + \bar{c}| = \sqrt{338}$.

If the lengths of three vectors $\bar{a}, \bar{b}$ and $\bar{c}$ are $5, 12, 13$ units respectively,and each one is perpendicular to the sum of the other two,then $|\bar{a}+\bar{b}+\bar{c}| = \dots$

Similar Questions

If $\vec{a}$ and $\vec{b}$ are two vectors such that $|\vec{a}|=2$,$|\vec{b}|=3$ and $\vec{a}+t \vec{b}$ and $\vec{a}-t \vec{b}$ are perpendicular,where $t$ is a positive scalar,then

If $i, j, k$ are unit orthonormal vectors and $a$ is a vector,if $a \times r = j$,then $a \cdot r$ is

If the vectors $\overline{a} = c(\log_7 x) \hat{i} + 2 \hat{j} + 3 \hat{k}$ and $\overline{b} = (\log_7 x) \hat{i} + 3c(\log_7 x) \hat{j} - 4 \hat{k}$ make an obtuse angle for any $x > 0$,then $c$ belongs to

Given the following simultaneous equations for vectors $x$ and $y$:
$(i) x + y = a$
$(ii) x \times y = b$
$(iii) x \cdot a = 1$
Then $x = ?, y = ?$

Let $v_1, v_2, v_3, v_4$ be unit vectors in the $XY$-plane,one each in the interior of the four quadrants. Which of the following statements is necessarily true?

Vedclass Test Series

Exam Paper Generator

Online Exam Module