Advertisements
Advertisements
Question
Projection vector of `vec"a"` on `vec"b"` is ______.
Options
`((vec"a"*vec"b")/|vec"b"|^2)vec"b"`
`(vec"a"*vec"b")/|vec"b"|`
`(vec"a"*vec"b")/|vec"a"|`
`((vec"a"*vec"b")/|vec"a"|^2)vec"b"`
Solution
Projection vector of `vec"a"` on `vec"b"` is `((vec"a"*vec"b")/|vec"b"|^2)vec"b"`.
Explanation:
Let `vec"a"` and `vec"b"` be two vectors represented by `vec"OA"` and `vec"OB"` respectively.
Now `vec"a"*vec"b" = |vec"a"||vec"b"| cos theta`
= `|vec"b"|(|vec"a"|costheta)`
= `|vec"b"|("OA" cos theta)`
= `|vec"b"|("OL")`
⇒ OL = `(vec"a" * vec"b")/|vec"b"|`
⇒ Projection of vector `vec"a"` on `vec"b" = (vec"a"*vec"b" vec"b")/(|vec"b"| |vec"b"|)`
= `(vec"a"*vec"b")/|vec"b"|^2 vec"b"`
APPEARS IN
RELATED QUESTIONS
Find the angle between the vectors `hati - 2hatj + 3hatk` and `3hati - 2hatj + hatk`.
Find the projection of the vector `hati - hatj` on the vector `hati + hatj`.
Find the projection of the vector `hati + 3hatj + 7hatk` on the vector `7hati - hatj + 8hatk`.
Show that `|veca|vecb+|vecb|veca` is perpendicular to `|veca|vecb-|vecb|veca,` for any two nonzero vectors `veca and vecb`.
If the vertices A, B, C of a triangle ABC are (1, 2, 3), (–1, 0, 0), (0, 1, 2), respectively, then find ∠ABC. [∠ABC is the angle between the vectors `bar(BA)` and `bar(BC)`].
Find the vector equation of the line passing through the point A(1, 2, –1) and parallel to the line 5x – 25 = 14 – 7y = 35z.
If P, Q and R are three collinear points such that \[\overrightarrow{PQ} = \vec{a}\] and \[\overrightarrow{QR} = \vec{b}\]. Find the vector \[\overrightarrow{PR}\].
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are non-coplanar vectors, prove that the points having the following position vectors are collinear: \[\vec{a,} \vec{b,} 3 \vec{a} - 2 \vec{b}\]
Using vector method, prove that the following points are collinear:
A (6, −7, −1), B (2, −3, 1) and C (4, −5, 0)
Using vector method, prove that the following points are collinear:
A (2, −1, 3), B (4, 3, 1) and C (3, 1, 2)
Using vector method, prove that the following points are collinear:
A (1, 2, 7), B (2, 6, 3) and C (3, 10, −1)
Let `veca` , `vecb` and `vecc` be three vectors such that `|veca| = 1,|vecb| = 2, |vecc| = 3.` If the projection of `vecb` along `veca` is equal to the projection of `vecc` along `veca`; and `vecb` , `vecc` are perpendicular to each other, then find `|3veca - 2vecb + 2vecc|`.
The projection of vector `vec"a" = 2hat"i" - hat"j" + hat"k"` along `vec"b" = hat"i" + 2hat"j" + 2hat"k"` is ______.
What is the angle between two vectors `veca` and `vecb` with magnitudes `sqrt(3)` and 2 respectively, such that `veca * vecb = sqrt(6)`
What is the angle between the vectors `hati - 2hatj + 3hatk` and `3hati - 2hatj + hatk`
What is the projection of vector `hati - hatj` on the vector `hati + hatj`.
If `veca` is a non zero vector of magnitude `a` and `lambda` `veca` non-zero scolor, then `lambda` is a unit vector of.
If `veca` and `vecb` are two vectors such that `|veca + vecb| = |vecb|`, then prove that `(veca + 2vecb)` is perpendicular to `veca`.
If `veca` and `vecb` are unit vectors and θ is the angle between them, then prove that `sin θ/2 = 1/2 |veca - vecb|`.
Write the projection of the vector `(vecb + vecc)` on the vector `veca`, where `veca = 2hati - 2hatj + hatk, vecb = hati + 2hatj - 2hatk` and `vecc = 2hati - hatj + 4hatk`.
Projection of vector `2hati + 3hatj` on the vector `3hati - 2hatj` is ______.
If `veca, vecb, vecc` are mutually perpendicular vectors of equal magnitudes, show that the vector `vecc* vecd = 15` is equally inclined to `veca, vecb "and" vecc.`
