Home
Class 12
MATHS
A line passes through the point with ...

A line passes through the point with position vector `2 hat i-3 hat j+4 hat k` and is in the direction of `3 hat i+4 hat j-5 hat kdot` Find the equations of the line in vector and Cartesian forms.

Text Solution

Verified by Experts

Since the line passes through `2hati-3hatj+4hatk` and has direction of `3hati+4hatj-5hatk`, its vector equation is
`" "vecr=hata+lamdahatbrArrvecr=2hati-3hatj+4hatk+lamda(3hati+4hatj-5hatk)`, where `lamda` is a parameter.`" "`(i)
Cartesian equivalent of (i) is `(x-2)/(3)=(y+3)/(4)=(z-4)/(-5)`
Promotional Banner

Similar Questions

Explore conceptually related problems

Find the projection of vector hat i+3 hat j+7 hat k on the vector 7 hat i- hat j+8 hat kdot

Find the projection of the vector hat i + 3 hat j + 7 hat k on the vector 7 hat i - hat j + 8 hat k .

Find the direction cosines of the vector hat i+2 hat j+3 hat kdot

If the four points with position vectors −2 hat i+ hat j+ hat k, hat i+ hat j + hat k, hat j – hat k and λ hat j+ hat k are coplanar, then λ=

Show that the points with position vectors 2 hat i + 6 hat j + 3 hat k , hat i + 2 hat j + 7 hat k and 3 hat i + 10 hat j - hat k are collinear.

Show that the points with the position vectors 2 hat i + 6 hat j + 3 hat k, hat i + 2 hat j + 7 hat k and 3 hat i + 10 hat j - hat k are collinear.

If the vector 8 hat i + a hat j of magnitude 10 is in the direction of the vector 4 hat i - 3 hat j , then the value of a is equal to

Find the projection of the vector vec alpha = 2 hat i + 3 hat j + 2 hat k on the vector vec b = hat i + 2 hat j + hat k .

The unit vector in the direction of the sum of vectors hat i + hat j + hat k and 2 hat i + 3 hat j + 4 hat k is