If a,b,c are the three vectors mutually perpendicular to each other and |a|=1,|b|=3 and |c|=5, then |a-2b,b-3c,c-4a| is equal to:

Question

If a,b,c are the three vectors mutually perpendicular to each other and |a|=1,|b|=3 and |c|=5, then |a-2b,b-3c,c-4a| is equal to: (A) 0 (B)  -24  (C) 3600 (D)  -215

Tardigrade Admin · Accepted Answer

[a-2b,b-3c,c-4a] =(a-2b). (b-3c)× (c-4a) =(a-2b). b× c-4b× a+12c× a =(a-2b).(a+4c+12b) =a.a-24b.b =1-24× 9 =1-216=-215

Q. If $a, b, c$ are the three vectors mutually perpendicular to each other and $∣ a ∣ = 1, ∣ b ∣ = 3$ and $∣ c ∣ = 5,$ then $∣ a - 2 b, b - 3 c, c - 4 a ∣$ is equal to:

0

$- 24$

3600

$- 215$

360

$[a - 2 b, b - 3 c, c - 4 a]$ $= (a - 2 b) . {(b - 3 c) \times (c - 4 a)}$ $= (a - 2 b) . {b \times c - 4 b \times a + 12 c \times a}$ $= (a - 2 b) . (a + 4 c + 12 b)$
$= a . a - 24 b . b$
$= 1 - 24 \times 9$
$= 1 - 216 = - 215$

Q. If a,b,c are the three vectors mutually perpendicular to each other and ∣a∣=1,∣b∣=3 and ∣c∣=5, then ∣a−2b,b−3c,c−4a∣ is equal to:

0

−24

3600

−215

360

[a−2b,b−3c,c−4a] =(a−2b).{(b−3c)×(c−4a)} =(a−2b).{b×c−4b×a+12c×a} =(a−2b).(a+4c+12b) =a.a−24b.b =1−24×9 =1−216=−215

Q. If $a, b, c$ are the three vectors mutually perpendicular to each other and $∣ a ∣ = 1, ∣ b ∣ = 3$ and $∣ c ∣ = 5,$ then $∣ a - 2 b, b - 3 c, c - 4 a ∣$ is equal to:

$- 24$

$- 215$

$[a - 2 b, b - 3 c, c - 4 a]$ $= (a - 2 b) . {(b - 3 c) \times (c - 4 a)}$ $= (a - 2 b) . {b \times c - 4 b \times a + 12 c \times a}$ $= (a - 2 b) . (a + 4 c + 12 b)$
$= a . a - 24 b . b$
$= 1 - 24 \times 9$
$= 1 - 216 = - 215$