The vector c cdot (b+c) times (a+b+c) is equa | vedclass

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

Question

(A) We need to evaluate the expression $c \cdot ((b+c) 	imes (a+b+c))$.Using the distributive property of the cross product,we have:$(b+c) 	imes (a+

Vedclass · Accepted Answer

$c \cdot (b 	imes a)$

Vedclass · Answer

(A) We need to evaluate the expression $c \cdot ((b+c) 	imes (a+b+c))$.Using the distributive property of the cross product,we have:$(b+c) 	imes (a+b+c) = b 	imes a + b 	imes b + b 	imes c + c 	imes a + c 	imes b + c 	imes c$.Since the cross product of any vector with itself is zero ($b 	imes b = 0$ and $c 	imes c = 0$),the expression simplifies to:$(b+c) 	imes (a+b+c) = b 	imes a + b 	imes c + c 	imes a + c 	imes b$.Now,taking the dot product with $c$:$c \cdot (b 	imes a + b 	imes c + c 	imes a + c 	imes b) = c \cdot (b 	imes a) + c \cdot (b 	imes c) + c \cdot (c 	imes a) + c \cdot (c 	imes b)$.Using the scalar triple product property $[x, y, z] = x \cdot (y 	imes z)$,we get:$= [c, b, a] + [c, b, c] + [c, c, a] + [c, c, b]$.Since any scalar triple product with two identical vectors is zero,we have:$[c, b, c] = 0$,$[c, c, a] = 0$,and $[c, c, b] = 0$.Thus,the expression simplifies to $[c, b, a] = c \cdot (b 	imes a)$.Since $c \cdot (b 	imes a) = -c \cdot (a 	imes b)$,and looking at the options,the correct form is $c \cdot (b 	imes a)$.

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

Similar Questions

Which of the following elements shows polymorphism?

The main organelle involved in the modification and routing of newly synthesized proteins to their destinations is

Which of the following is not an antibiotic?

If $q$ is false and $p \wedge q \leftrightarrow r$ is true,then which one of the following statements is a tautology?

Which one of the following pairs is correctly matched with regard to the codon and the amino acid coded by it?

Vedclass Test Series

Exam Paper Generator

Online Exam Module