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Vector Algebra

Question
CBSEENMA12036079

Let ABCD be a parallelogram such that AB with rightwards arrow on top space equals space straight q with rightwards arrow on top comma space AD with rightwards arrow on top space equals space straight p with rightwards arrow on top and ∠BAD be an acute angle. If straight r with rightwards arrow on top  is the vector that coincides with the altitude directed from the vertex B the side AD, then straight r with rightwards arrow on top is given byLet ABCD be a parallelogram such that AB = q,AD = p and ∠BAD be an acute angle. If r is the vector that coincides with the altitude directed from the vertex B to the side AD, then r is given by (1)

  • straight r with rightwards arrow on top space equals space 3 straight q with rightwards arrow on top space minus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals negative space straight q with rightwards arrow on top space plus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals space straight q with rightwards arrow on top space minus fraction numerator open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
  • straight r with rightwards arrow on top space equals space 3 straight q with rightwards arrow on top space minus fraction numerator 3 open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top

Solution

D.

straight r with rightwards arrow on top space equals space 3 straight q with rightwards arrow on top space minus fraction numerator 3 open parentheses straight p with rightwards arrow on top stack. straight q with rightwards arrow on top close parentheses over denominator straight p with rightwards arrow on top straight p with rightwards arrow on top end fraction straight p with rightwards arrow on top
AE with rightwards arrow on top space equals space vector space component space of space straight q with rightwards arrow on top space on space straight p with rightwards arrow on top

AE with rightwards arrow on top space equals fraction numerator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis over denominator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis end fraction straight p with rightwards arrow on top
therefore space From space increment ABE comma AB with rightwards arrow on top space plus BE with rightwards arrow on top space equals space AE with rightwards arrow on top
rightwards double arrow space straight q with rightwards arrow on top space plus straight r with rightwards arrow on top space equals space fraction numerator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis over denominator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis end fraction straight p with rightwards arrow on top
rightwards double arrow straight r with rightwards arrow on top space equals space minus straight q with rightwards arrow on top space fraction numerator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis over denominator left parenthesis straight p with rightwards arrow on top. straight q with rightwards arrow on top right parenthesis end fraction straight p with rightwards arrow on top

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