Rustic Linen Tablecloth, Example 6 - Line through (5, 2, -4), parallel to 3i + 2j - 8k. About featured snippets•FeedbackQuestions & answersStack ExchangeQuestionI am give the point (1,0,−3) and the vector 2i−4j+5kFind the equation of the line parallel to vector and passing through point (1,0,−3)Could one use the fact that the dot product between the line and the vector?Please give me some direction as where to go for this question. I am so lostAnswer · 5 votesIn general, we know that the equation of the line passing through the point (x1,y1,z1) & parallel to the vector (ai+bj+ck) is given as x−x1a=y−y1b=z−z1cHence, the equation of the line passing through the point (1,0,−3) & parallel to the vector (2i−4j+5k) is given as x−12=y−0−4=z−(−3)5x−12=−y4=z+35It can also be represented asr(t)=(1,0,−3)+t(2,−4,5)MoreCheggQuestionFind a vector equation for the line through the point P = (4, 2, 4) and parallel to the vector v = < -2, -5, -3 > . Assume r(0) = 4i + 2j + 4k and that v is the direction vector of the line. R(t) = Rewrite this in terms of the corresponding parametric equations for the line. x = y = z = Write symmetric equations for the line in the form of x-4/4 = y-40/b =Answer · 0 votesThe vector equation for the line through the point and parallel to the vector is . Find the v.MoreStudy.comQuestionWrite the vector equation of the line through the point __(2;4)__ and parallel to the vector __b.Answer · 0 votesOur line must pass through the point (2,4), so we have r→0=⟨2,4⟩. Then we know that our line is parallel to the vectorb→=i^−j^=⟨1,−1⟩Note that since our line must be parallel to this, it is our direction vector, i.e. v→=⟨1,−1⟩. So the vector equation for the line isr→(t)=⟨2,4⟩+t⟨1,−1⟩=⟨2+t(1), 4+t(−1)⟩=⟨2+t,4−t⟩=(2+t) i^+(4−t) j^MoreQuoraQuestionA line passes through the point (1,-5,2) and is parallel to the vector R=2i-3j-k. What is the vector equation of the line?Answer · 1 voteL: (1, –5, 2) + t (2, –3, –1)MoreTopprQuestionFind the vector equation of the passing through the point 2i + 3j + k and parallel to the vector 4i - 2j + 3k .Answer · 224 votesThe line passes through the point,vec a= 2vec i + 3vec j + vec kAnd parallel to the line,vec b= 4vec i - 2vec j + 3vec kThe vector equation of the line passing through apoint and parallel to the given line is,vec r= vec a + lambdavec bSubstituting the values, we get,vec r= ( 2vec i+ 3vec j+vec k ) + lambda ( 4vec i- 2vec j+ 3vec k )vec r= ( 2 + 4lambda )vec i + ( 3 - 2lambda )vec j + ( 1 + 3lambda )vec kMoreWyzantQuestionFind a vector equation with parameter t for the line through the point (9,0,−3) ( 9 , 0 , − 3 ) and parallel to the vector 2−4+3.Answer · 0 votesThe parametric equations for the line in question arex =9 + 2ty = -4tz = -3 +3t and the vector valued function r(t)r(t) = < 9 + 2t, -4t, -3+3t >MoreSocraticQuestionHow do you write the vector equation that passes through point (-1,4) and parallel to <6,-10>?Answer · 0 votes→r=(−14)+λ(6−10)Explanation:The vector equation of a line in the direction of →D passing through the point →A is:→r=→A+λ→DSo the required equation in vector form is:→r=(−14)+λ(6−10)Alternative notations are:→r=⟨−1,4⟩+λ⟨6,−10⟩Or,→r=(−1ˆi+4ˆj)+λ(6ˆi−10ˆj)MoreStudySmarter USQuestionFind a vector equation for a line through the point (0,14,−10) and parallel to the line x=−1+2t,y=6−3t,z=3+9t and the parametric equations for a line through the point (0,14,−10) and parallel to the line x=−1+2t,y=6−3t,z=3+9t.Answer · 0 votesThe vector equation for a line through the point ((0,14, - 10)) and parallel to the line (x = - 1 + 2t,y = 6 - 3t,z = 3 + 9t) is (2ti + (14 - 3t)j + ( - 10 + 9t)k).The parametric equations for a line through the point ((0,14, - 10)) and parallel to the line (x = - 1 + 2t,y = 6 - 3t,z = 3 + 9t) are (x = 2t,y = 14 - 3t,z = - 10 + 9t)MoreDoubtnutQuestionFind the vector equation of a line through the point (-3, 2, -4) and is parallel to the vector 3hati + 2hatj+ 4hatk.Answer · 366 votesAnswer: vecr = (-3hati+2hatj-4hatk)+lambda(3hati + 2hatj + 4hatk)MoreBrainly.comQuestionFind a vector equation and parametric equations for the line. 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The line through the point (0, 11, −8) and parallel to the line x = −1 + 4t, y = 6 − 3t, z = 3 + 7tAnswer · 6 votesThe vector parametric equation of the line parallel to the given one and that passes through the point (0, 11, −8) is:Finding the parallel line.If you recall to 2-dimensional lines, two lines are parallel if the lines have the same rate of change.The same happens here, if each variable has the same rate of change, then the lines will be parallel.So if we want parametric equation of a line parallel to:x = −1 + 4t, y = 6 − 3t, z = 3 + 7tWe must have:x = a + 4t, y = b - 3t, z = c + 7tNow, if we want this line to pass through the point (0, 11, -8), then we can replace the correspondent values in the constant term for each equation:This is the parametric equation of the line parallel to the given one and that passes through the point (0, 11, −8) If you want to learn more about parametric equations, you can read:https://brainly.com/question/12695467More Feedback Como Sacarse Un Pedazo De Muela, Find a vector equation for the line through the point P = (4 .. 1 answerThe vector equation for the line through the point P = ( 4 , 2 , 4 ) and parallel to the vector v =< − 2 , − 5 , − 3 > is r ( t ) = P + t v . Find the v. Clay Linen Duvet Cover, Example 0.1. Vector equation of a line.. PDFFind a vector equation for the line through (4,6,-3) and parallel to v = 5i - 10j + 2k. Solution: With the identifications x0 = 4,y0 = 6,z0 = -3,a = 5,b .4 pages Corduroy Sac, Write the vector equation of the line through the point __(2;4). Determine a vector equation for the line through the points (-1, 4) and (2, -1). Find the symmetric equation for the line that passes through the point (4,-2,6) .1 answer  ·  Top answer: Our line must pass through the point (2,4), so we have r→0=⟨2,4⟩. Then we know that our line is parallel to the vectorb→=i^−j^=⟨1,−1⟩ . Linen Duvet Cover Rust, 12.5 Lines and Planes. In fact a line can be defined and uniquely identified by providing one point on the line and a vector parallel to the line (in one of two possible directions). Kenny Adidas Nmd, What is the vector equation of a straight line passing .. 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