Let $\vec a = 2\hat i + {\lambda _1}\hat j + 3\hat k$, $\vec b = 4\hat i + \left( {3 - {\lambda _2}} \right)\hat j + 6\hat k,{\rm{\;and\;}}\vec c = 3\hat i + 6\hat j + \left( {{\lambda _3} - 1} \right)\hat k$ be three vectors such that $\vec b = 2\vec a\;{\rm{and\;\vec a\;is\;perpendicular\;to\;}}\vec c$. Then a possible value of (λ1, λ2, λ3) is:

Question

Let $\vec a = 2\hat i + {\lambda _1}\hat j + 3\hat k$, $\vec b = 4\hat i + \left( {3 - {\lambda _2}} \right)\hat j + 6\hat k,{\rm{\;and\;}}\vec c = 3\hat i + 6\hat j + \left( {{\lambda _3} - 1} \right)\hat k$ be three vectors such that $\vec b = 2\vec a\;{\rm{and\;\vec a\;is\;perpendicular\;to\;}}\vec c$. Then a possible value of (λ1, λ­2, λ3) is:

TuteeHUB · Accepted Answer

$\left( {\frac{1}{2},4, - 2} \right)$

TuteeHUB · Answer

(1, 3, 1)

TuteeHUB · Answer

$\left( { - \frac{1}{2},\;4,\;0} \right)$

TuteeHUB · Answer

(1, 5, 1)

1.	Let \(\vec a = 2\hat i + {\lambda _1}\hat j + 3\hat k\), \(\vec b = 4\hat i + \left( {3 - {\lambda _2}} \right)\hat j + 6\hat k,{\rm{\;and\;}}\vec c = 3\hat i + 6\hat j + \left( {{\lambda _3} - 1} \right)\hat k\) be three vectors such that \(\vec b = 2\vec a\;{\rm{and\;\vec a\;is\;perpendicular\;to\;}}\vec c\). Then a possible value of (λ1, λ2, λ3) is:
A.	(1, 3, 1)
B.	\(\left( { - \frac{1}{2},\;4,\;0} \right)\)
C.	\(\left( {\frac{1}{2},4, - 2} \right)\)
D.	(1, 5, 1)
Answer» C. \(\left( {\frac{1}{2},4, - 2} \right)\)

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