A line passes through the point (3,4,5) and is parallel to the vector `(2hat(i) +2hat(j) -3hat(k))` . Find the equations of the line in the vector as

Monjur Alahi

A line passes through the point (3,4,5) and is parallel to the vector `(2hat(i) +2hat(j) -3hat(k))` . Find the equations of the line in the vector as well as Cartesian forms.


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Salim Ahmed Kawsar

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Correct Answer - `vec(r )=(2hat(i)+4hat(j)+5hat(k)) +lambda(2hat(i) +2hat(j)-3hat(k)) ,(x-3)/(2)=(y-4)/(2)=(z-5)/(-3)`

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Find the value of `lambda` for which the four points with position vectors `(hat(i)+2hat(j)+3hat(k)), (3hat(i)-hat(j)+2hat(k)), (-2hat(i)+lambda hat(j

Correct Answer - `lambda=3`

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A line passes through the point (2,1,-3) and is parallel to the vector `(hat(i) -2hat(j) +2hat(k))` . Find the equations of the line in vector and Car

Correct Answer - `vec(r )=(2hat(i)-hat(j)-3hat(k)) +lambda (hat(i) -2hat(j)+3hat(k)) ,(x-2)/(1)=(y-1)/(-2)=(z+3)/(3)`

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Find the vector equations of the line passing through the point with position vector `(2hat(i) +hat(j) -5hat(k))` and parallel to the vector `(hat(i)

Correct Answer - `vec(r ) =(2hat(i) +hat(j) -5hat(k)) +lambda(hat(i) +3hat(j)-hat(k)) ,(x-2)/(1)=(y-1)/(3)=(z+5)/(-1)`

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A line is drawn in the direction of `(hat(i) +hat(j) -2hat(k))` and it passes through a point with position vector `(2hat(i) -hat(j) - 4hat(k))` .Find

Correct Answer - `vec(r )=(2hat(i) -hat(j) +4hat(k)) +lambda(hat(i)-hat(j)-2hat(k)) ,(x-2)/(1)=(y+1)/(1)=(z-4)/(-2)`

2 Answers 1 views
`vec(r ) =(3hat(i) +hat(j)-2hat(k)) +lambda (hat(i)-hat(j)-2hat(k)) " and " vec(r ) =(2hat(i) -hat(j) -5hat(k)) + mu (3hat(i) -5hat(j) -4hat(k))` FInd

Correct Answer - `cos^(-1) .((8sqrt(3))/(15))`

2 Answers 1 views
`vec(r )=(hat(i) +hat(j)) +lambda(2hat(i) -hat(j) +hat(k))` `vec(r )=(2hat(i) +hat(j) -hat(k)) + mu (3hat(i) -5hat(j) +2hat(k))`

Correct Answer - `(10)/(sqrt(59))` units

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`vec(r )=(-4hat(i)+4hat(j) +hat(k)) + lambda (hat(i) +hat(j) -hat(k))` `vec(r)=(-3hat(i) -8hat(j) -3hat(k)) + mu (2hat(i) +3hat(j) +3hat(k))`

Correct Answer - `sqrt(62)` units

2 Answers 1 views
`vec(r ) =(hat(i) +2hat(j) +3hat(k)) + lambda(hat(i) -3hat(j) +2hat(k))` `vec(r ) =(4hat(i) +5hat(j) +6hat(k)) + mu (2hat(i) + hat(j) +2hat(k))` Find

Correct Answer - `(3sqrt(19))/(19)` units

2 Answers 1 views
`vec(r ) =(hat(i)+2hat(j) -4hat(k)) + lambda(2hat(i) +3hat(j) +6hat(k))` `vec(r )=(3hat(i) +3hat(j) -5hat(k)) + mu (-2hat(i) +3hat(j) +8hat(k))`

Correct Answer - `(14sqrt(241))/(241)` units

2 Answers 1 views
Show that the lines `vec( r)=(2hat(i) -3hat(k)) + lambda(hat(i) +2hat(j)+3hat(k)) " and " vec(r )=(3hat(i) +6hat(j)+3hat(k)) + mu(2hat(i) +3hat(j) +4h

Correct Answer - `(2,6,3)`

2 Answers 1 views
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