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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
In a trapezium, the vector $\overrightarrow {BC} = \lambda \overrightarrow {AD} .$ We will then find that $p = \overrightarrow {AC} + \overrightarrow {BD} $ is collinear with $\overrightarrow {AD} ,$ If $p = \mu \overrightarrow {AD} ,$ then
  • ✓
    $\mu = \lambda + 1$
  • B
    $\lambda = \mu + 1$
  • C
    $\lambda + \mu = 1$
  • D
    $\mu = 2 + \lambda $
✓

Answer

Correct option: A.
$\mu = \lambda + 1$
a
(a) We have, $p = \overrightarrow {AC} + \overrightarrow {BD} = \overrightarrow {AC} + \overrightarrow {BC} + \overrightarrow {CD} = \overrightarrow {AC} + \lambda \overrightarrow {AD} + \overrightarrow {CD} $

$ = \lambda \,\overrightarrow {AD} + (\overrightarrow {AC} + \overrightarrow {CD} ) = \lambda \,\overrightarrow {AD} + \overrightarrow {AD} = (\lambda + 1)\overrightarrow {AD} .$

Therefore $p = \mu \overrightarrow {AD} \Rightarrow \mu = \lambda + 1.$

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