Advertisements
Advertisements
प्रश्न
Select the correct option from the given alternatives:
The volume of tetrahedron whose vectices are (1,-6,10), (-1, -3, 7), (5, -1, λ) and (7, -4, 7) is 11 cu units, then the value of λ is
पर्याय
7
2
1
5
उत्तर
7
APPEARS IN
संबंधित प्रश्न
if `veca = 2hati - hatj - 2hatk " and " vecb = 7hati + 2hatj - 3hatk`, , then express `vecb` in the form of `vecb = vec(b_1) + vec(b_2)`, where `vec(b_1)` is parallel to `veca` and `vec(b_2)` is perpendicular to `veca`
If \[\overrightarrow{a}\] and \[\overrightarrow{b}\] denote the position vectors of points A and B respectively and C is a point on AB such that 3AC = 2AB, then write the position vector of C.
Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].
Find a unit vector in the direction of the vector \[\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + 6 \hat{k}\].
Find the value of 'p' for which the vectors \[3 \hat{i} + 2 \hat{j} + 9 \hat{k}\] and \[\hat{i} - 2p \hat{j} + 3 \hat{k}\] are parallel.
If \[\vec{a} , \vec{b}\] are the vectors forming consecutive sides of a regular hexagon ABCDEF, then the vector representing side CD is
If O and O' are circumcentre and orthocentre of ∆ ABC, then \[\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}\] equals
Find the components along the coordinate axes of the position vector of the following point :
S(4, –3)
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.
Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).
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:
If l, m, n are direction cosines of a line then `"l"hat
"i" + "m"hat"j" + "n"hat"k"` 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"`
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.
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" xx 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" xx bar"b").(bar"c"xxbar"d")`
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")`
The XZ plane divides the line segment joining the points (3, 2, b) and (a, -4, 3) in the ratio ______.
The points A(- a, -b), B (0, 0), C(a, b) and D(a2 , ab) are ______.
If `overline"u"` and `overline"v"` are unit vectors and θ is the acute angle between them, then `2overline"u" xx 3overline"v"` is a unit vector for ______
For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______
Find the unit vector in the direction of the sum of the vectors `vec"a" = 2hat"i" - hat"j" + 2hat"k"` and `vec"b" = -hat"i" + hat"j" + 3hat"k"`.
The area of the parallelogram whose adjacent sides are `hat"i" + hat"k"` and `2hat"i" + hat"j" + hat"k"` is ______.
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 ______.
If `veca` and `vecb` are unit vectors, then what is the angle between `veca` and `vecb` for `sqrt(3) veca - vecb` to be a unit vector?
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"`
If `vec"a", vec"b", vec"c"` determine the vertices of a triangle, show that `1/2[vec"b" xx vec"c" + vec"c" xx vec"a" + vec"a" xx vec"b"]` gives the vector area of the triangle. Hence deduce the condition that the three points `vec"a", vec"b", vec"c"` are collinear. Also find the unit vector normal to the plane of the triangle.
The formula `(vec"a" + vec"b")^2 = vec"a"^2 + vec"b"^2 + 2vec"a" xx vec"b"` is valid for non-zero vectors `vec"a"` and `vec"b"`
The unit vector perpendicular to the vectors `6hati + 2hatj + 3hatk` and `3hati - 6hatj - 2hatk` is
For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = - hati + hatj - hatk` find the unit vector in the direction of the vector `veca + vecb`.
Check whether the vectors`2hati+2hatj+3hatk,-3hati+3hatj+2hatk and 3hati +4hatk` form a triangle or not.
In the triangle PQR, `bb(bar(PQ) = 2 bara)` and `bb(bar(QR) = 2 barb)`. The mid-point of PR is M. Find the following vectors in terms of `bb(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.
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)`