Let u, v, w be vectors such that u + v + w = | vedclass

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

Question

(B) Given that $u + v + w = 0$. Taking the dot product of the sum with itself: $(u + v + w) \cdot (u + v + w) = 0 \cdot 0 = 0$. Expanding the dot prod

Vedclass · Accepted Answer

$-25$

Vedclass · Answer

(B) Given that $u + v + w = 0$. Taking the dot product of the sum with itself: $(u + v + w) \cdot (u + v + w) = 0 \cdot 0 = 0$. Expanding the dot product: $u \cdot u + v \cdot v + w \cdot w + 2(u \cdot v + v \cdot w + w \cdot u) = 0$. Using the property $|a|^2 = a \cdot a$,we have $|u|^2 + |v|^2 + |w|^2 + 2(u \cdot v + v \cdot w + w \cdot u) = 0$. Substitute the given magnitudes: $3^2 + 4^2 + 5^2 + 2(u \cdot v + v \cdot w + w \cdot u) = 0$. $9 + 16 + 25 + 2(u \cdot v + v \cdot w + w \cdot u) = 0$. $50 + 2(u \cdot v + v \cdot w + w \cdot u) = 0$. $2(u \cdot v + v \cdot w + w \cdot u) = -50$. Therefore,$u \cdot v + v \cdot w + w \cdot u = -25$.

Let $u, v, w$ be vectors such that $u + v + w = 0$. If $|u| = 3, |v| = 4,$ and $|w| = 5,$ find the value of $u \cdot v + v \cdot w + w \cdot u$.

Similar Questions

$A$ vector coplanar with the non-collinear vectors $\vec{a}$ and $\vec{b}$ is:

$<2, 2, 2> = \ldots \ldots$

The vectors $\vec{AB} = 3\hat{i} + 4\hat{k}$ and $\vec{AC} = 5\hat{i} - 2\hat{j} + 4\hat{k}$ are the sides of a $\triangle ABC$. The length of the median through $A$ is:

$A$ vector $\vec{r}$ has magnitude $14$ and direction ratios $2, 3, -6$. Find the direction cosines and components of $\vec{r}$,given that $\vec{r}$ makes an acute angle with the $x$-axis.

Let $\bar{a}$ and $\bar{b}$ be the position vectors of points $A$ and $B$ respectively. $C$ and $D$ are points on the line $AB$ such that $\overline{AC} = 3 \overline{AB}$ and $\overline{BD} = 2 \overline{BA}$. Find the vector $\overline{CD}$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module