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".(bar"b" xx bar"c")`
उत्तर
This is the scalar product of two vectors. Therefore, this expression is meaningful and it is a scalar.
APPEARS IN
संबंधित प्रश्न
If D, E, F are the mid-points of the sides BC, CA and AB respectively of a triangle ABC, write the value of \[\overrightarrow{AD} + \overrightarrow{BE} + \overrightarrow{CF} .\]
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.
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 \[\overrightarrow{b} = 2 \hat{i} + \hat{j} - 7 \hat{k}\].
Find the value of 'p' for which the vectors \[3 \hat{i} + 2 \hat{j} + 9 \hat{k}\] and \[\hat{i} - 2p \hat{j} + 3 \hat{k}\] are parallel.
Let G be the centroid of ∆ ABC. If \[\overrightarrow{AB} = \vec{a,} \overrightarrow{AC} = \vec{b,}\] then the bisector \[\overrightarrow{AG} ,\] in terms of \[\vec{a}\text{ and }\vec{b}\] is
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.
Find a unit vector perpendicular to each of the vectors `veca + vecb "and" veca - vecb "where" veca = 3hati + 2hatj + 2hatk and vecb = i + 2hatj - 2hatk`
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 given figure express `bar"c"` and `bar"d"` in terms of `bar"a"` and `bar"b"`.
Express `- hat"i" - 3hat"j" + 4hat"k"` as the linear combination of the vectors `2hat"i" + hat"j" - 4hat"k", 2hat"i" - hat"j" + 3hat"k"` and `3hat"i" + hat"j" - 2hat"k"`
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:
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
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"`.
Find the component form of `bar"a"` if it lies in YZ-plane makes 60° with positive Y-axis and `|bar"a"| = 4`.
Dot product of a vector with vectors `3hat"i" - 5hat"k", 2hat"i" + 7hat"j" and hat"i" + hat"j" + hat"k"` are respectively -1, 6 and 5. Find the vector.
Express `hat"i" + 4hat"j" - 4hat"k"` as the linear combination of the vectors `2hat"i" - hat"j" + 3hat"k", hat"i" - 2hat"j" + 4hat"k"` and `- hat"i" + 3hat"j" - 5hat"k"`.
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"`
For any vectors `bar"a", bar"b", bar"c"` show that `(bar"a" + bar"b" + bar"c") xx bar"c" + (bar"a" + bar"b" + bar"c") xx bar"b" + (bar"b" - bar"c") xx bar"a" = 2bar"a" xx bar"c"`
If `overline"u"` and `overline"v"` are unit vectors and θ is the acute angle between them, then `2overline"u" xx 3overline"v"` is a unit vector for ______
For any vector `overlinex` the value of `(overlinex xx hati)^2 + (overlinex xx hatj)^2 + (overlinex xx hatk)^2` is equal to ______
lf `overlinea`, `overlineb` and `overlinec` are unit vectors such that `overlinea + overlineb + overlinec = overline0` and angle between `overlinea` and `overlineb` is `pi/3`, then `|overlinea xx overlineb| + |overlineb xx overlinec| + |overlinec xx overlinea|` = ______
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 `hat"b" = 2hat"i" + hat"j" - 2hat"k"`, find the unit vector in the direction of `2vec"a" - vec"b"`
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 ______.
Classify the following measures as scalar and vector.
40°
Classify the following as scalar and vector quantity.
Distance
If `veca ≠ vec(0), veca.vecb = veca.vecc, veca xx vecb = veca xx vecc`, then show that `vecb = vecc`.
Let `bara, barb` and `barc` be three vectors, then `bara xx (barb xx barc) = (bara xx barb) xx barc` if
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
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`
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.
If `|veca| = 3, |vecb| = sqrt(2)/3` and `veca xx vecb` is a unit vector then the angle between `veca` and `vecb` will be ______.
lf ΔABC is an equilateral triangle and length of each side is “a” units, then the value of `bar(AB)*bar(BC) + bar(BC)*bar(CA) + bar(CA)*bar(AB)` is ______.
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"`.
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.
