જો vec{A} = hat{i} - 2hat{j} - 3hat{k},vec{B} | vedclass

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

Question

(A) સૌ પ્રથમ,સદિશ ગુણાકાર $\vec{A} 	imes \vec{B}$ શોધો:$\vec{A} 	imes \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -2 & -3 \ 2 & 1

Vedclass · Accepted Answer

$5(-\hat{i} + 3\hat{j} + 4\hat{k})$

Vedclass · Answer

(A) સૌ પ્રથમ,સદિશ ગુણાકાર $\vec{A} 	imes \vec{B}$ શોધો:$\vec{A} 	imes \vec{B} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 1 & -2 & -3 \ 2 & 1 & -1 \end{vmatrix}$$= \hat{i}(2 - (-3)) - \hat{j}(-1 - (-6)) + \hat{k}(1 - (-4))$$= \hat{i}(5) - \hat{j}(5) + \hat{k}(5) = 5\hat{i} - 5\hat{j} + 5\hat{k}$હવે,$(\vec{A} 	imes \vec{B}) 	imes \vec{C}$ શોધો:$(\vec{A} 	imes \vec{B}) 	imes \vec{C} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ 5 & -5 & 5 \ 1 & 3 & -2 \end{vmatrix}$$= \hat{i}(10 - 15) - \hat{j}(-10 - 5) + \hat{k}(15 - (-5))$$= \hat{i}(-5) - \hat{j}(-15) + \hat{k}(20)$$= -5\hat{i} + 15\hat{j} + 20\hat{k}$$= 5(-\hat{i} + 3\hat{j} + 4\hat{k})$

જો $\vec{A} = \hat{i} - 2\hat{j} - 3\hat{k}$,$\vec{B} = 2\hat{i} + \hat{j} - \hat{k}$,અને $\vec{C} = \hat{i} + 3\hat{j} - 2\hat{k}$ હોય,તો $(\vec{A} \times \vec{B}) \times \vec{C} = \dots$

Similar Questions

$i \times (j \times k) + j \times (k \times i) + k \times (i \times i)$ ની કિંમત શું થાય?

જો $a=2 \hat{i}-3 \hat{j}+\hat{k}$, $b=\hat{i}-\hat{j}+2 \hat{k}$ અને $c=2 \hat{i}+\hat{j}+\hat{k}$ ત્રણ સદિશો હોય, તો $|(a \times b) \times c|=$

વિધાન $(A)$ : જો $\vec{a}$ એ $\vec{b}$ અને $\vec{c}$ ને લંબ હોય,તો $\vec{a} \times (\vec{b} \times \vec{c}) = 0$.
કારણ $(R)$ : જો $\vec{b}$ એ $\vec{c}$ ને લંબ હોય,તો $\vec{b} \times \vec{c} = 0$.

Vedclass Test Series

Exam Paper Generator

Online Exam Module