[(vec{a} times vec{b}) times (vec{a} times ve | vedclass

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

Question

(A) Let $\vec{x} = \vec{a} 	imes \vec{b}$. Then the expression is $(\vec{x} 	imes (\vec{a} 	imes \vec{c})) \cdot \vec{d}$.Using the vector triple p

Vedclass · Accepted Answer

$(\vec{a} \cdot \vec{d}) [\vec{a} \vec{b} \vec{c}]$

Vedclass · Answer

(A) Let $\vec{x} = \vec{a} 	imes \vec{b}$. Then the expression is $(\vec{x} 	imes (\vec{a} 	imes \vec{c})) \cdot \vec{d}$.Using the vector triple product formula $(\vec{A} 	imes \vec{B}) 	imes \vec{C} = (\vec{A} \cdot \vec{C})\vec{B} - (\vec{B} \cdot \vec{C})\vec{A}$,we have:$(\vec{a} 	imes \vec{b}) 	imes (\vec{a} 	imes \vec{c}) = [(\vec{a} 	imes \vec{b}) \cdot \vec{c}]\vec{a} - [(\vec{a} 	imes \vec{b}) \cdot \vec{a}]\vec{c}$.Since $[(\vec{a} 	imes \vec{b}) \cdot \vec{a}] = 0$ (as the scalar triple product with two identical vectors is zero),the expression simplifies to:$[\vec{a} \vec{b} \vec{c}]\vec{a}$.Now,taking the dot product with $\vec{d}$:$([\vec{a} \vec{b} \vec{c}]\vec{a}) \cdot \vec{d} = [\vec{a} \vec{b} \vec{c}] (\vec{a} \cdot \vec{d})$.Thus,the correct option is $A$.

$[(\vec{a} \times \vec{b}) \times (\vec{a} \times \vec{c})] \cdot \vec{d} = \dots$

Similar Questions

If $[(\overline{a}+2 \overline{b}+3 \overline{c}) \times(\overline{b}+2 \overline{c}+3 \overline{a})] \cdot(\overline{c}+2 \overline{a}+3 \overline{b})=54$,then the value of $[\overline{a} \ \overline{b} \ \overline{c}]$ is

If the volume of a tetrahedron,whose vertices are $A(1, 2, 3)$,$B(-3, -1, 1)$,$C(2, 1, 3)$,and $D(-1, 2, x)$ is $\frac{11}{6}$ cubic units,then the value of $x$ is:

If the vectors $i+3j-2k$,$2i-j+4k$ and $3i+2j+xk$ are coplanar,then the value of $x$ is:

$(a+b) \cdot(b+c) \times(a+b+c)$ is equal to

The value of $(\vec{a} + 2\vec{b} - \vec{c}) \cdot \{(\vec{a} - \vec{b}) \times (\vec{a} - \vec{b} - \vec{c})\}$ is equal to

Vedclass Test Series

Exam Paper Generator

Online Exam Module