Advertisements
Advertisements
प्रश्न
In Figure, which of the following is not true?
पर्याय
\[\overrightarrow{AB} + \overrightarrow{BC} + \overrightarrow{CA} = \vec{0}\]
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{AC} = \vec{0}\]
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \vec{0}\]
\[\overrightarrow{AB} - \overrightarrow{CB} + \overrightarrow{CA} = \vec{0}\]
उत्तर
\[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \vec{0}\]
We have, LHS = \[\overrightarrow{AB} + \overrightarrow{BC} - \overrightarrow{CA} = \overrightarrow{AC} - \overrightarrow{CA}\] [∵ \[\overrightarrow{AB} + \overrightarrow{BC} = \overrightarrow{AC}\]
\[= - \overrightarrow{CA} - \overrightarrow{CA} \]
\[ = - 2 \overrightarrow{CA}\]
So, LHS \[\neq\] RHS
Hence, It is not true.
APPEARS IN
संबंधित प्रश्न
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 \[\vec{a} + \vec{b} + \vec{c} .\]
Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].
Find the position vector of the mid-point of the line segment AB, where A is the point (3, 4, −2) and B is the point (1, 2, 4).
Write a unit vector in the direction of the sum of the vectors \[\overrightarrow{a} = 2 \hat{i} + 2 \hat{j} - 5 \hat{k}\] and \[\overrightarrow{b} = 2 \hat{i} + \hat{j} - 7 \hat{k}\].
If ABCDEF is a regular hexagon, then \[\overrightarrow{AD} + \overrightarrow{EB} + \overrightarrow{FC}\] equals
ABCD is a parallelogram with AC and BD as diagonals.
Then, \[\overrightarrow{AC} - \overrightarrow{BD} =\]
Find the vector equation of the plane through the line of intersection of the planes x + y + z = 1 and 2x + 3y + 4z = 5 which is perpendicular to the plane x – y + z = 0. Hence find whether the plane thus obtained contains the line \[\frac{x + 2}{5} = \frac{y - 3}{4} = \frac{z}{5}\] or not.
Find the components along the coordinate axes of the position vector of the following point :
P(3, 2)
If `veca` and `vecb` are non- collinear vectors, find the value of x such that the vectors `barα = (x - 2)veca + vecb` and `barβ = (3+2x)bara - 2barb` are collinear.
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.
The vector `bar"a"` is directed due north and `|bar"a"|` = 24. The vector `bar"b"` is directed due west and `|bar"b"| = 7`. Find `|bar"a" + bar"b"|`.
OABCDE is a regular hexagon. The points A and B have position vectors `bar"a"` and `bar"b"` respectively referred to the origin O. Find, in terms of `bar"a"` and `bar"b"` the position vectors of C, D and E.
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj + 2hatk` and `3hati + 4hatk` form a triangle or not.
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
A point P with position vector `(- 14hat"i" + 39hat"j" + 28hat"k")/5` divides the line joining A (1, 6, 5) and B in the ratio 3 : 2, then find the point B.
If ABC is a triangle whose orthocentre is P and the circumcentre is Q, prove that `bar"PA" + bar"PB" + bar"PC" = 2bar"PQ".`
If a parallelogram is constructed on the vectors `bar"a" = 3bar"p" - bar"q", bar"b" = bar"p" + 3bar"q" and |bar"p"| = |bar"q"| = 2` and angle between `bar"p" and bar"q"` is `pi/3,` and angle between lengths of the sides is `sqrt7 : sqrt13`.
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")`
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 ______.
For any non-zero vectors a and b, [b a × b a] = ?
a and b are non-collinear vectors. If c = (x - 2)a + b and d = (2x + 1)a - b are collinear vectors, then the value of x = ______.
For 0 < θ < π, if A = `[(costheta, -sintheta), (sintheta, costheta)]`, then ______
If the points (–1, –1, 2), (2, m, 5) and (3,11, 6) are collinear, find the value of m.
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 ______.
Find the unit vector in the direction of the sum of the vectors `vec"a" = 2hat"i" - hat"j" + hat"k"` and `vec"b" = 2hat"j" + hat"k"`.
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 ______.
If `veca` and `vecb` are two collinear vectors then which of the following are incorrect.
Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is ______.
In the triangle PQR, `bar(PQ) = 2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bar a and bar b `.
- `bar("PR")`
- `bar("PM")`
- `bar("QM")`
Check whether the vectors `2hati + 2hatj + 3hat k, -3hati + 3hatj + 2hat k` and `3hati + 4hatk` form a triangle or not.
Find the value of λ for which the points (6, – 1, 2), (8, – 7, λ) and (5, 2, 4) are collinear.
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.
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.
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
