If M1, M2, M3 and M4, are respectively the magnitudes of the vectors a1=2 hat i - hat j + hat k a 2=-3 hat i -4 hat j -4 hat k , a 3=- hat i + hat j - hat k a 4=- hat i +3 hat j + hat k , then the correct order of M1, M2, M3 and M4 is

Question

If M1, M2, M3 and M4, are respectively the magnitudes of the vectors a1=2 hat i - hat j + hat k a 2=-3 hat i -4 hat j -4 hat k , a 3=- hat i + hat j - hat k a 4=- hat i +3 hat j + hat k , then the correct order of M1, M2, M3 and M4 is (A) M3 < M1 < M4 < M2 (B) M3 < M1 < M2 < M4 (C) M3 < M4 < M1 < M 2 (D) M3 < M4 < M2 < M1

Tardigrade Admin · Accepted Answer

Given that, a 1=2 hat i - hat j + hat k a 2 =3 hat i -4 hat j -4 hat k a 3 =- hat i + hat j - hat k a 4 =- hat i +3 hat j + hat k M =| a | M1 =| a 1|=|2 hat i - hat j + hat k | =√(2)2+(-1)2+(1)2 =√4+1+1=√6 =|3 hat i -4 hat j -4 hat k | =√(3)2+(-4)2+(-4)2 =√9+16+16=√41 M3 =|- i + hat j - hat k | =√(-1)2+(1)2+(-1)2 =√1+1+1=√3 M4 =|- hat i +3 hat j + hat k | =√(-1)2+(3)2+(-1)2 =√1+9+1=√11 Hence, the correct order of magnitudes M3 < M1 < M4 < M2

$M_{3} < M_{1} < M_{4} < M_{2}$

$M_{3} < M_{1} < M_{2} < M_{4}$

$M_{3} < M_{4} < M_{1} < M_{2}$

$M_{3} < M_{4} < M_{2} < M_{1}$

Q. If M1​,M2​,M3​ and M4​, are respectively the magnitudes of the vectors a1​=2i^−j^​+k^ a2​=−3i^−4j^​−4k^,a3​=−i^+j^​−k^ a4​=−i^+3j^​+k^, then the correct order of M1​,M2​,M3​ and M4​ is

M3​<M1​<M4​<M2​

M3​<M1​<M2​<M4​

M3​<M4​<M1​<M2​

M3​<M4​<M2​<M1​

$M_{3} < M_{1} < M_{4} < M_{2}$

$M_{3} < M_{1} < M_{2} < M_{4}$

$M_{3} < M_{4} < M_{1} < M_{2}$

$M_{3} < M_{4} < M_{2} < M_{1}$