If veca+2 vecb+3 vecc = vec0, then veca × vecb+ vecb × vecc+ vecc × veca=

Question

If veca+2 vecb+3 vecc = vec0, then veca × vecb+ vecb × vecc+ vecc × veca= (A) 0 (B) 6( vecb × vecc) (C) 2( vecb × vecc) (D) 3( vecb × vecc)

Tardigrade Admin · Accepted Answer

veca+2 vecb+3 vecc=0 ⇒ veca=-2 vecb-3 vecc veca × vecb+ vecb × vecc+ vecc × veca =(-2 vecb-3 vecc) × vecb+ vecb × vecc+ vecc ×(-2 vecb-3 vecc) =-2( vecb × vecb)-3( vecc × vecb)+ vecb × vecc-2( vecc × vecb)-3( vecc × vecc) =-0+3( vecb × vecc)+ vecb × vecc+2( vecb × vecc)+0 =6( vecb × vecc)

Q. If $a + 2 b + 3 c = 0$ , then $a \times b + b \times c + c \times a =$

0

$6 (b \times c)$

$2 (b \times c)$

$3 (b \times c)$

Q. If a+2b+3c=0, then a×b+b×c+c×a=

0

6(b×c)

2(b×c)

3(b×c)

a+2b+3c=0 ⇒a=−2b−3c a×b+b×c+c×a =(−2b−3c)×b+b×c+c×(−2b−3c) =−2(b×b)−3(c×b)+b×c−2(c×b)−3(c×c) =−0+3(b×c)+b×c+2(b×c)+0 =6(b×c)

Q. If $a + 2 b + 3 c = 0$ , then $a \times b + b \times c + c \times a =$

$6 (b \times c)$

$2 (b \times c)$

$3 (b \times c)$