Advertisements
Advertisements
प्रश्न
If \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] represent the sides of a triangle taken in order, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]
उत्तर
Let ABC be a triangle such that \[\overrightarrow{BC} = \vec{a} , \overrightarrow{CA} = \vec{b}\] and \[\overrightarrow{AB} = \vec{c} .\]
Then,
\[\vec{a} + \vec{b} + \vec{c} = \overrightarrow{BC} + \overrightarrow{CA} + \overrightarrow{AB}\]
\[= \overrightarrow{BA} + \overrightarrow{AB} \]
\[ = \vec{0}\] [∵ \[\overrightarrow{BC} + \overrightarrow{CA} = \overrightarrow{BA}\]
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 \[\vec{a}\], \[\vec{b}\], \[\vec{c}\] are the position vectors of the vertices of an equilateral triangle whose orthocentre is at the origin, then write the value of \[\vec{a} + \vec{b} + \vec{c} .\]
If a vector makes angles α, β, γ with OX, OY and OZ respectively, then write the value of sin2 α + sin2 β + sin2 γ.
Write the position vector of a point dividing the line segment joining points having position vectors \[\hat{i} + \hat{j} - 2 \hat{k} \text{ and }2 \hat{i} - \hat{j} + 3 \hat{k}\] externally in the ratio 2:3.
If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} - 3 \hat{k} \text{ and }\overrightarrow{b} = 2 \hat{i} + 4 \hat{j} + 9 \hat{k} ,\] find a unit vector parallel to \[\overrightarrow{a} + \overrightarrow{b}\].
If G is the intersection of diagonals of a parallelogram ABCD and O is any point, then \[O \vec{A} + O \vec{B} + O \vec{C} + O \vec{D} =\]
If O and O' are circumcentre and orthocentre of ∆ ABC, then \[\overrightarrow{OA} + \overrightarrow{OB} + \overrightarrow{OC}\] equals
If ABCDEF is a regular hexagon, then \[\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}\] equals
Find the components along the coordinate axes of the position vector of the following point :
P(3, 2)
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj + 2hatk` and `3hati + 4hatk` form a triangle or not.
In the given figure express `bar"c"` and `bar"d"` in terms of `bar"a"` and `bar"b"`.
Find the distance from (4, - 2, 6) to each of the following:
(a) The XY-plane
(b) The YZ-plane
(c) The XZ-plane
(d) The X-axis
(e) The Y-axis
(f) The Z-axis.
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 the sum of two unit vectors is itself a unit vector, then the magnitude of their difference is ______.
Select the correct option from the given alternatives:
Let a, b, c be distinct non-negative numbers. If the vectors `"a"hat"i" + "a"hat"j" + "c"hat"k" , hat"i" + hat"k" "and" "c"hat"i" + "c"hat"j" + "b"hat"k"` lie in a plane, then c is
ABCD is a parallelogram. E, F are the midpoints of BC and CD respectively. AE, AF meet the diagonal BD at Q and P respectively. Show that P and Q trisect DB.
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"`.
Find the acute angle between the curves at their points of intersection, y = x2, y = x3.
Let bar"b" = 4hat"i" + 3hat"j" and bar"c" be two vectors perpendicular to each other in the XY-plane. Find the vector in the same plane having projection 1 and 2 along bar"b" and bar"c" respectively.
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" xx(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".bar"b") xx (bar"c".bar"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"`
The vector eqliation of line 2x - 2 = 3y + 1 = 6z - 2 is
lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______
If the points (–1, –1, 2), (2, m, 5) and (3,11, 6) are collinear, find the value of m.
If `|vec"a"|` = 3 and –1 ≤ k ≤ 2, then `|"k"vec"a"|` lies in the interval ______.
Find a unit vector in the direction of `vec"PQ"`, where P and Q have co-ordinates (5, 0, 8) and (3, 3, 2), respectively
The vector `vec"a" + vec"b"` bisects the angle between the non-collinear vectors `vec"a"` and `vec"b"` if ______.
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"`
Classify the following as scalar and vector quantity.
Force
In Figure, identify the following vector.
Collinear but not equal
Four vectors `veca, vecb, vecc` and `vecx` satisfy the relation `(veca.vecx)vecb = vecc + vecx` where `vecb * veca` ≠ 1. The value of `vecx` in terms of `veca, vecb` and `vecc` is equal to
Check whether the vectors `2hati + 2hatj + 3hat k, -3hati + 3hatj + 2hat k` 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.
If A(1, 2, – 3) and B(– 1, – 2, 1) are the end points of a vector `vec("AB")` then find the unit vector in the direction of `vec("AB")`.
If `hata` is unit vector and `(2vecx - 3hata)*(2vecx + 3hata)` = 91, find the value of `|vecx|`.
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 `2 hati+2 hatj+3 hatk,-3 hati+3 hatj+2 hatk and 3 hati +4 hatk` form a triangle or not.
Consider the following statements and choose the correct option:
Statement 1: If `veca` and `vecb` represents two adjacent sides of a parallelogram then the diagonals are represented by `veca + vecb` and `veca - vecb`.
Statement 2: If `veca` and `vecb` represents two diagonals of a parallelogram then the adjacent sides are represented by `2(veca + vecb)` and `2(veca - vecb)`.
Which of the following is correct?
