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STD 12 - 10. vector algebra — Mathematics STD 12 Science — Question

CBSE BoardEnglish MediumSTD 12 ScienceMathematicsSTD 12 - 10. vector algebra1 Mark
MCQ
If $\vec r = 3\hat i+ 2\hat j +5\hat k\,\,,\vec a= 2\hat i-\hat j +\hat k,\,\,\vec b= \hat i+ 3\hat j -2\hat k$ and $\vec c =-2\hat i +\hat j -3\hat k$ such that $\vec r=\lambda \vec a+\mu \vec b+\gamma \vec c$, then -
  • ✓
    $\mu,\frac{\lambda}{2},\gamma$ are in $A.P$
  • B
    $2\mu,\lambda,\gamma$ are in $A.P$
  • C
    $\mu,\lambda,\gamma$ are in $A.P$
  • D
    $\lambda,\frac{\mu}{3},\gamma$ are in $A.P$
✓

Answer

Correct option: A.
$\mu,\frac{\lambda}{2},\gamma$ are in $A.P$
a
$3 \hat{i}+2 \hat{j}-5 \hat{k}$

$=(2 \lambda+\mu-2 \gamma) \hat{\mathrm{i}}+(-\lambda+3 \mu+\gamma) \hat{\mathrm{j}}+(\lambda-2 \mu-3 \gamma) \hat{\mathrm{k}}$

$\therefore \quad 2 \lambda+\mu-2 \gamma=3$

$-\lambda+3 \mu+\gamma=2$

$\lambda-2 \mu-3 \gamma=-5$

$\therefore \quad \mu=1, \gamma=4, \lambda=5$

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