Advertisements
Advertisements
प्रश्न
The 2 vectors `hat"j" + hat"k"` and `3hat"i" - hat"j" + 4hat"k"` represents the two sides AB and AC, respectively of a ∆ABC. The length of the median through A is ______.
विकल्प
`sqrt(34)/2`
`sqrt(48)/2`
`sqrt(18)`
None of these
उत्तर
The 2 vectors `hat"j" + hat"k"` and `3hat"i" - hat"j" + 4hat"k"` represents the two sides AB and AC, respectively of a ∆ABC. The length of the median through A is `sqrt(34)/2`.
Explanation:
Median `vec"AD"` is given by
`|vec"AD"| = 1/2 |3hat"i" + hat"j" + 5hat"k"|`
= `sqrt(34)/2`
APPEARS IN
संबंधित प्रश्न
If \[\overrightarrow{a}\] is a non-zero vector of modulus a and m is a non-zero scalar such that m \[\overrightarrow{a}\] is a unit vector, write the value of m.
Write a unit vector making equal acute angles with the coordinates axes.
Forces 3 O \[\vec{A}\], 5 O \[\vec{B}\] act along OA and OB. If their resultant passes through C on AB, then
If points A (60 \[\hat{i}\] + 3 \[\hat{j}\]), B (40 \[\hat{i}\] − 8 \[\hat{j}\]) and C (a \[\hat{i}\] − 52 \[\hat{j}\]) are collinear, then a is equal to
If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then \[O \vec{A} + O \vec{B} + O \vec{C} + O \vec{D} =\]
Find the value of λ for which the four points with position vectors `6hat"i" - 7hat"j", 16hat"i" - 19hat"j" - 4hat"k" , lambdahat"j" - 6hat"k" "and" 2hat"i" - 5hat"j" + 10hat"k"` are coplanar.
Find the coordinates of the point which is located in the YZ-plane, one unit to the right of the XZ- plane, and six units above the XY-plane.
Express `- hat"i" - 3hat"j" + 4hat"k"` as the linear combination of the vectors `2hat"i" + hat"j" - 4hat"k", 2hat"i" - hat"j" + 3hat"k"` and `3hat"i" + hat"j" - 2hat"k"`
If `|bara|` = 3, `|barb|` = 5, `|barc|` = 7 and `bara + barb + barc = bar0`, then the angle between `bara` and `barb` is ______.
Select the correct option from the given alternatives:
Let α, β, γ be distinct real numbers. The points with position vectors `alphahat"i" + betahat"j" + gammahat"k", betahat"i" + gammahat"j" + alphahat"k", gammahat"i" + alphahat"j" + betahat"k"`
Select the correct option from the given alternatives:
If `bar"a", bar"b", bar"c"` are non-coplanar unit vectors such that `bar"a"xx (bar"b"xxbar"c") = (bar"b"+bar"c")/sqrt2`, then the angle between `bar"a" "and" bar"b"` is
Two sides of a parallelogram are `3hat"i" + 4hat"j" - 5hat"k"` and `-2hat"j" + 7hat"k"`. Find the unit vectors parallel to the diagonals.
Express the vector `bar"a" = 5hat"i" - 2hat"j" + 5hat"k"` as a sum of two vectors such that one is parallel to the vector `bar"b" = 3hat"i" + hat"k"` and other is perpendicular to `bar"b"`.
Show that the vector area of a triangle ABC, the position vectors of whose vertices are `bar"a", bar"b" and bar"c"` is `1/2[bar"a" xx bar"b" + bar"b" xx bar"c" + bar"c" xx bar"a"]`.
State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:
`bar"a".(bar"b" + bar"c")`
State whether the expression is meaningful. If not, explain why? If so, state whether it is a vector or a scalar:
`bar"a". bar"b" + bar"c"`
For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______
Using vectors, prove that cos (A – B) = cosA cosB + sinA sinB.
The angle between the vectors `hat"i" - hat"j"` and `hat"j" - hat"k"` is ______.
If `vec"a" = hat"i" + hat"j" + 2hat"k"` and `hat"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `2vec"a" - vec"b"`
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
If `vec"r" * vec"a" = 0, vec"r" * vec"b" = 0` and `vec"r" * vec"c" = 0` for some non-zero vector `vec"r"`, then the value of `vec"a" * (vec"b" xx vec"c")` is ______.
Let `veca, vecb` and `vecc` be three unit vectors such that `veca xx (vecb xx vecc) = sqrt(3)/2 (vecb + vecc)`. If `vecb` is not parallel to `vecc`, then the angle between `veca` and `vecc` is
Let the vectors `vec(a)` such `vec(b)` that `|veca|` = 3 and `|vecb| = sqrt(2)/3`, then `veca xx vecb` is a unit vector if the angle between `veca` and `vecb` is
The angles of a triangle, two of whose sides are represented by the vectors `sqrt(3)(veca xx vecb)` and `vecb - (veca.vecb)veca` where `vecb` is a non-zero vector and `veca` is a unit vector are ______.
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
Check whether the vectors `2hati+2hatj+3hatk,-3hati+3hatj+2hatk` and `3hati+4hatk` form a triangle or not.
In the triangle PQR, `bar(PQ)`= 2`bar a` and `bar(QR)`= 2`bar b` . The mid-point of PR is M. Find following vectors in terms of `bara` and `barb`.
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`
Check whether the vectors `2hati + 2hatj +3hatk, - 3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
