Advertisements
Advertisements
प्रश्न
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")`
उत्तर
This is vector product of two vectors. Therefore, this expression is meaningful and it is a vector.
APPEARS IN
संबंधित प्रश्न
If \[\vec{a}\] and \[\vec{b}\] represent two adjacent sides of a parallelogram, then write vectors representing its diagonals.
If G denotes the centroid of ∆ABC, then write the value of \[\overrightarrow{GA} + \overrightarrow{GB} + \overrightarrow{GC} .\]
If \[\overrightarrow{a} = \hat{i} + \hat{j} , \vec{b} = \hat{j} + \hat{k} \text{ and }\vec{c} = \hat{k} + \hat{i} ,\] write unit vectors parallel to \[\overrightarrow{a} + \overrightarrow{b} - 2 \overrightarrow{c} .\]
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.
Find a unit vector in the direction of \[\overrightarrow{a} = 2 \hat{i} - 3 \hat{j} + 6 \hat{k}\].
Find a unit vector in the direction of the vector \[\overrightarrow{a} = 3 \hat{i} - 2 \hat{j} + 6 \hat{k}\].
Write a unit vector in the direction of \[\overrightarrow{PQ}\], where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.
If \[\vec{a} , \vec{b}\] are the vectors forming consecutive sides of a regular hexagon ABCDEF, then the vector representing side CD is
Forces 3 O \[\vec{A}\], 5 O \[\vec{B}\] act along OA and OB. If their resultant passes through C on AB, then
The position vectors of the points A, B, C are \[2 \hat{i} + \hat{j} - \hat{k} , 3 \hat{i} - 2 \hat{j} + \hat{k}\text{ and }\hat{i} + 4 \hat{j} - 3 \hat{k}\] respectively.
These points
If three points A, B and C have position vectors \[\hat{i} + x \hat{j} + 3 \hat{k} , 3 \hat{i} + 4 \hat{j} + 7 \hat{k}\text{ and }y \hat{i} - 2 \hat{j} - 5 \hat{k}\] respectively are collinear, then (x, y) =
ABCD is a parallelogram with AC and BD as diagonals.
Then, \[\overrightarrow{AC} - \overrightarrow{BD} =\]
If \[\vec{a}\text{ and }\vec{b}\] are two collinear vectors, then which of the following are incorrect?
Find the components along the coordinate axes of the position vector of the following point :
P(3, 2)
If` vec"a" = 2hat"i" + 3hat"j" + + hat"k", vec"b" = hat"i" - 2hat"j" + hat"k" "and" vec"c" = -3hat"i" + hat"j" + 2hat"k", "find" [vec"a" vec"b" vec"c"]`
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.
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:
If `bar"a" "and" bar"b"` are unit vectors, then what is the angle between `bar"a"` and `bar"b"` for `sqrt3bar"a" - bar"b"` to be a unit vector?
If `bar"OA" = bar"a" and bar"OB" = bar"b",` then show that the vector along the angle bisector of ∠AOB is given by `bar"d" = lambda(bar"a"/|bar"a"| + bar"b"/|bar"b"|).`
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 `bar"a", bar"b", bar"c"` are unit vectors such that `bar"a" + bar"b" + bar"c" = bar0,` then find the value of `bar"a".bar"b" + bar"b".bar"c" + bar"c".bar"a".`
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".bar"b").bar"c"`
If the vectors `xhat"i" - 3hat"j" + 7hat"k" and hat"i" + "y"hat"j" - "z"hat"k"` are collinear then the value of `"xy"^2/"z"` is equal.
Find a vector of magnitude 11 in the direction opposite to that of `vec"PQ"` where P and Q are the points (1, 3, 2) and (–1, 0, 8), respectively.
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 `vec"a"` is any non-zero vector, then `(vec"a" .hat"i")hat"i" + (vec"a".hat"j")hat"j" + (vec"a".hat"k")hat"k"` equals ______.
Classify the following measures as scalar and vector.
40°
In Figure, identify the following vector.
Equal
If two or more vectors are parallel to the same line, such vectors are known as:
For given vectors, `veca = 2hati - hatj + 2hatk` and `vecb = - hati + hatj - hatk` find the unit vector in the direction of the vector `veca + vecb`.
If `veca` and `vecb` are two collinear vectors then which of the following are incorrect.
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.
