Advertisements
Advertisements
Question
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"`
Solution
This is the sum of scalar and vector which is not defined. Therefore, this expression is meaningless.
APPEARS IN
RELATED QUESTIONS
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 the position vector of a point dividing the line segment joining points A and B with position vectors \[\vec{a}\] and \[\vec{b}\] externally in the ratio 1 : 4, where \[\overrightarrow{a} = 2 \hat{i} + 3 \hat{j} + 4 \hat{k} \text{ and }\overrightarrow{b} = - \hat{i} + \hat{j} + \hat{k} .\]
If \[\overrightarrow{a} = \hat{i} + 2 \hat{j} , \vec{b} = \hat{j} + 2 \hat{k} ,\] write a unit vector along the vector \[3 \overrightarrow{a} - 2 \overrightarrow{b} .\]
Write a unit vector in the direction of \[\overrightarrow{a} = 3 \hat{i} + 2 \hat{j} + 6 \hat{k} .\]
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).
If \[\overrightarrow{a} = x \hat{i} + 2 \hat{j} - z \hat{k}\text{ and }\overrightarrow{b} = 3 \hat{i} - y \hat{j} + \hat{k}\] are two equal vectors, then write the value of x + y + z.
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 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 three units behind the YZ-plane, four units to the right of XZ-plane, and five units above the XY-plane.
If the sum of two unit vectors is itself a unit vector, then the magnitude of their difference 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.
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.
If P is orthocentre, Q is the circumcentre and G is the centroid of a triangle ABC, then prove that `bar"QP" = 3bar"QG"`.
Find two unit vectors each of which makes equal angles with bar"u", bar"v" and bar"w" where bar"u" = 2hat"i" + hat"j" - 2hat"k", bar"v" = hat"i" + 2hat"j" - 2hat"k", bar"w" = 2hat"i" - 2hat"j" + hat"k".
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.
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"|(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 ______.
a and b are non-collinear vectors. If p = (2x + 1) a - band q = (x - 2)a +b are collinear vectors, then x = ______.
For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______
If A, B, C and D are (3, 7, 4), (5, -2, - 3), (- 4, 5, 6) and(1, 2, 3) respectively, then the volume of the parallelopiped with AB, AC and AD as the co-terminus edges, is ______ cubic units.
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.
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 `vec"a" = hat"i" + hat"j" + 2hat"k"` and `vec"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `6vec"b"`
If two or more vectors are parallel to the same line, such vectors are known as:
Find `|vecx|` if `(vecx - veca).(vecx + veca)` = 12, where `veca` is a unit vector.
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj +2 hatk and 3hati + 4hatk` from 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.
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)`
In the triangle PQR, `bar"PQ" = bar"2a", bar"QR" = bar"2b"`. The midpoint of PR is M. Find the following vectors in terms of `bar"a"` and `bar"b"`:
(i) `bar"PR"` (ii) `bar"PM"` (iii) `bar"QM"`.
In the triangle PQR, `bar(PQ) = 2bara and bar(QR) = 2barb`. The mid-point of PR is M. Find the following vectors in terms of `bara and barb`.
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`
