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" xx bar"c")`
Solution
This is the scalar product of two vectors. Therefore, this expression is meaningful and it is a scalar.
APPEARS IN
RELATED QUESTIONS
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 \[\vec{a}\] and \[\vec{b}\] represent two adjacent sides of a parallelogram, then write vectors representing its diagonals.
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.
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
Find the position vector of the mid-point of the vector joining the points
Show that the four points having position vectors
\[6 \hat { i} - 7 \hat { j} , 16 \hat {i} - 19 \hat {j}- 4 \hat {k} , 3 \hat {j} - 6 \hat {k} , 2 \hat {i} + 5 \hat {j} + 10 \hat {k}\] are not coplanar.
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.
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"]`
ABCDEF is a regular hexagon. Show that `bar"AB" + bar"AC" + bar"AD" + bar"AE" + bar"AF" = 6bar"AO"`, where O is the centre of the hexagon.
Find the area of the traingle with vertices (1, 1, 0), (1, 0, 1) and (0, 1, 1).
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?
Select the correct option from the given alternatives:
The value of `hat"i".(hat"j" xx hat"k") + hat"j".(hat"i" xx hat"k") + hat"k".(hat"i" xx hat"j")` 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 a unit vector perpendicular to the plane containing the point (a, 0, 0), (0, b, 0) and (0, 0, c). What is the area of the triangle with these vertices?
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") 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")`
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 points A(- a, -b), B (0, 0), C(a, b) and D(a2 , ab) are ______.
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.
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 any non zero vector, a, b, c a · ((b + c) × (a + b + c)] = ______.
If `|vec"a"|` = 3 and –1 ≤ k ≤ 2, then `|"k"vec"a"|` lies in the interval ______.
Using vectors, find the value of k such that the points (k, – 10, 3), (1, –1, 3) and (3, 5, 3) are collinear.
The values of k for which `|"k"vec"a"| < |vec"a"|` and `"k"vec"a" + 1/2 vec"a"` is parallel to `vec"a"` holds true are ______.
If `vec"a"` and `vec"b"` are adjacent sides of a rhombus, then `vec"a" * vec"b"` = 0
Classify the following measures as scalar and vector.
40 watt
Which of the following measures as vector?
Find `|vecx|` if `(vecx - veca).(vecx + veca)` = 12, where `veca` is a unit vector.
Check whether the vectors `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk` and `3hati + 4hatk` form a triangle or not.
Check whether the vectors `2hati + 2 hatj + 3hatk, - 3hati + 3hatj + 2hatk and 3hati + 4hatk` From a triangle or not.
In the triangle PQR, `bar(PQ)=2bara` and `bar(QR)=2barb`. The mid-point of PR is M. Find following vectors in terms of `bara and barb`.
(i) `bar(PR)` (ii) `bar(PM)` (iii) `bar(QM)`
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 `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.
