Advertisements
Advertisements
Question
If `|vec"a"|` = 8, `|vec"b"|` = 3 and `|vec"a" xx vec"b"|` = 12, then value of `vec"a" * vec"b"` is ______.
Options
`6sqrt(3)`
`8sqrt(3)`
`12sqrt(3)`
None of these
Solution
If `|vec"a"|` = 8, `|vec"b"|` = 3 and `|vec"a" xx vec"b"|` = 12, then value of `vec"a" * vec"b"` is `12sqrt(3)`.
Explanation:
Using the formula `|vec"a" xx vec"b"| = |vec"a"|*|vec"b"| |sintheta|`
We get `theta = +- pi/6`.
Therefore, `vec"a"*vec"b" = |vec"a"|*|vec"b"| costheta`
= `8 xx 3 xx sqrt(3)/2`
= `12sqrt(3)`.
APPEARS IN
RELATED QUESTIONS
Write a unit vector in the direction of \[\overrightarrow{b} = 2 \hat{i} + \hat{j} + 2 \hat{k}\].
In a triangle OAC, if B is the mid-point of side AC and \[\overrightarrow{OA} = \overrightarrow{a} , \overrightarrow{OB} = \overrightarrow{b}\], then what is \[\overrightarrow{OC}\].
If points A (60 \[\hat{i}\] + 3 \[\hat{j}\]), B (40 \[\hat{i}\] − 8 \[\hat{j}\]) and C (a \[\hat{i}\] − 52 \[\hat{j}\]) are collinear, then a is equal to
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) =
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 a vector in the direction of `bara = hati - 2hatj` that has magnitude 7 units.
Select the correct option from the given alternatives:
If `|bar"a"| = 3` and - 1 ≤ k ≤ 2, then `|"k"bar"a"|` lies in the interval
Let `bara = hati - hatj, barb = hatj - hatk, barc = hatk - hati.` If `bard` is a unit vector such that `bara * bard = 0 = [(barb, barc, bard)]`, then `bard` equals ______.
In a parallelogram ABCD, diagonal vectors are `bar"AC" = 2hat"i" + 3hat"j" + 4hat"k" and bar"BD" = - 6hat"i" + 7hat"j" - 2hat"k"`, then find the adjacent side vectors `bar"AB" and bar"AD"`.
If ABC is a triangle whose orthocentre is P and the circumcentre is Q, prove that `bar"PA" + bar"PB" + bar"PC" = 2bar"PQ".`
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") 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")`
Find the volume of the parallelopiped spanned by the diagonals of the three faces of a cube of side a that meet at one vertex of the cube.
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.
The angle between the vectors `hat"i" - hat"j"` and `hat"j" - hat"k"` is ______.
The unit vector perpendicular to the vectors `hat"i" - hat"j"` and `hat"i" + hat"j"` forming a right handed system is ______.
`bara, barb` and `barc` are three vectors such that `veca + vecb + vecc` 20, `|bara| = 1, |barb| = 2` and `|barc| = 3`. Then `bara. barb + barb.barc + bar(c.a)` is equal to
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
If `veca` and `vecb` are two collinear vectors then which of the following are incorrect.
Find `|vecx|`, if for a unit vector `veca, (vecx - veca) * (vecx + veca)` = 12
Find `|veca xx vecb|`, if `veca = hati - 7hatj + 7hatk` and `vecb = 3hati - 2hatj + 2hatk`
Unit vector along `vec(PQ)`, where coordinates of P and Q respectively are (2, 1, – 1) and (4, 4, – 7), is ______.
Check whether the vectors `2hati + 2hatj + 3hatk, - 3hati + 3hatj +2 hatk and 3hati + 4hatk` from 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 `2hati + 2hatj + 3hatk, -3hati + 3hatj + 2hatk and 3hati + 4hatk` form a triangle or not.
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)`
