text: # If vector  vec a = hati + hatj + hatk , vecb = 4 hati + 3 hatj + 4 hatk  and  vec c = hati + alpha hatj + beta hatk  are linearly dependent and  | vec c | = sqrt3  , then value of  | alpha | + | beta |  is
  
  Updated On: 17-04-2022
  
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  Text Solution
  
  2314
  
  A
  Solution :
  vec(a) , vec(b) , vec(c) are linerly depend rArr Coplanar vectors <br> |{:(,1,1,1),(,4,3,4),(,1,alpha,beta):}|=0 <br> rArr 1 + 0 - beta =0 rArr beta = 1 <br> because |vec C| = sqrt(3) rArr 1 + alpha^(2) + beta alpha = pm 1 rArr |alpha | +| beta| = 2
explanation: The document contains a math question related to linear dependence of vectors and the magnitude of a vector. It also includes a detailed solution to the problem, leading to the answer.
distilabel_metadata.content: Evaluate the user given text extract and determine if it contains a math question and optionally and answer to this question.
  
  Output rules:
  
  1. Briefly describe the document and mention if it contains a question or a question and answer.
  2. Finalize the output with: Label: no-question,question,question-and-answer,multiple-question,multiple-question-and-answer
distilabel_metadata.role: system
distilabel_metadata.content: # If vector  vec a = hati + hatj + hatk , vecb = 4 hati + 3 hatj + 4 hatk  and  vec c = hati + alpha hatj + beta hatk  are linearly dependent and  | vec c | = sqrt3  , then value of  | alpha | + | beta |  is
  
  Updated On: 17-04-2022
  
  Get Answer to any question, just click a photo and upload the photo
  and get the answer completely free,
  
  Watch 1000+ concepts & tricky questions explained!
  
  Click here to get PDF DOWNLOAD for all questions and answers of this chapter - VIDYAMANDIR CLASSES (VMC MODULES) Class 12 JEE MAIN REVISION TEST - 30 | JEE -2020
  
  Text Solution
  
  2314
  
  A
  Solution :
  vec(a) , vec(b) , vec(c) are linerly depend rArr Coplanar vectors <br> |{:(,1,1,1),(,4,3,4),(,1,alpha,beta):}|=0 <br> rArr 1 + 0 - beta =0 rArr beta = 1 <br> because |vec C| = sqrt(3) rArr 1 + alpha^(2) + beta alpha = pm 1 rArr |alpha | +| beta| = 2
distilabel_metadata.role: user
distilabel_metadata.raw_output_q_a_detector_0: The document contains a math question related to linear dependence of vectors and the magnitude of a vector. It also includes a detailed solution to the problem, leading to the answer.
  
  Label: question-and-answer