If vec{A}, vec{B} and vec{C} are vectors havi | vedclass

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

Question

(B) Given that $\vec{A} + \vec{B} + \vec{C} = \vec{0}$.Squaring both sides,we get:$(\vec{A} + \vec{B} + \vec{C}) \cdot (\vec{A} + \vec{B} + \vec{C}) =

Vedclass · Accepted Answer

$-1.5$

Vedclass · Answer

(B) Given that $\vec{A} + \vec{B} + \vec{C} = \vec{0}$.Squaring both sides,we get:$(\vec{A} + \vec{B} + \vec{C}) \cdot (\vec{A} + \vec{B} + \vec{C}) = 0$$|\vec{A}|^2 + |\vec{B}|^2 + |\vec{C}|^2 + 2(\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}) = 0$Since the vectors have unit magnitude,$|\vec{A}| = |\vec{B}| = |\vec{C}| = 1$.Substituting these values:$1^2 + 1^2 + 1^2 + 2(\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}) = 0$$3 + 2(\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}) = 0$$2(\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}) = -3$$\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A} = -1.5$

If $\vec{A}, \vec{B}$ and $\vec{C}$ are vectors having unit magnitude. If $\vec{A} + \vec{B} + \vec{C} = \vec{0}$,then $\vec{A} \cdot \vec{B} + \vec{B} \cdot \vec{C} + \vec{C} \cdot \vec{A}$ will be:

Similar Questions

The vectors $\overrightarrow P = a\hat i + a\hat j + 3\hat k$ and $\overrightarrow Q = a\hat i - 2\hat j - \hat k$ are perpendicular to each other. The positive value of $a$ is

Define the scalar product and obtain the magnitude of a vector from it. Mention the direction of scalar product.

Find the unit vector perpendicular to $\vec{A}$ and $\vec{B}$ where $\vec{A} = \hat{i} - 2\hat{j} + \hat{k}$ and $\vec{B} = \hat{i} + 2\hat{j}$.

Which of the following is the unit vector perpendicular to $\vec{A}$ and $\vec{B}$?

$A$ vector $\vec{A}$ points towards North and vector $\vec{B}$ points upwards,then $\vec{A} \times \vec{B}$ points towards ...........

Vedclass Test Series

Exam Paper Generator

Online Exam Module