# 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
The text passage contains a mathematical question involving vectors and their properties, followed by a detailed solution that leads to the answer.
single_question_with_answer
Given a text passage, determine:
    1. If it contains a mathematical question (including word problems or calculations)
    2. If an answer to that mathematical question is provided in the text

First, describe the content structure you found in 1-2 sentences.

Then provide your analysis in the following format:
TYPE: <one of the following values>
- NO_QUESTION
- SINGLE_QUESTION
- SINGLE_QUESTION_WITH_ANSWER
- MULTIPLE_QUESTIONS
- MULTIPLE_QUESTIONS_WITH_ANSWERS
system
# 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
user
The text passage contains a mathematical question involving vectors and their properties, followed by a detailed solution that leads to the answer.

TYPE: SINGLE_QUESTION_WITH_ANSWER