Advertisements
Advertisements
Question
Suppose `bar"a" = bar"0"`:
If `bar"a" xx bar"b" = bar"a" xx bar"c"`, then is `bar"b" = bar"c"` ?
Advertisements
Solution
Take `bar"b" = hat"i", bar"c" = hat"j"`
Then `bar"a" xx bar"b" = bar"a" xx bar"c" = 0`, but `bar"b" ne bar"c"`
APPEARS IN
RELATED QUESTIONS
Find the scalar components and magnitude of the vector joining the points `P(x_1, y_1, z_1) and Q (x_2, y_2, z_2).`
Find the area of a parallelogram whose adjacent sides are represented by the vectors\[2 \hat{i} - 3 \hat{k} \text { and } 4 \hat{j} + 2 \hat{k} .\]
Suppose `bar"a" = bar"0"`:
If `bar"a".bar"b" = bar"a".bar"c"`, then is `bar"b" = bar"c"` ?
Suppose `bar"a" = bar"0"`:
If `bar"a".bar"b" = bar"a".bar"c" and bar"a" xx bar"b" = bar"a" xx bar"c"`, then is `bar"b" = bar"c"`?
A(2, 3), B(−1, 5), C(−1, 1) and D(−7, 5) are four points in the Cartesian plane, Check if, `bar("CD")` is parallel to `bar("AB")`
If `bar("a") = 4hat"i" + 3hat"k"` and `bar("b") = -2hat"i" + hat"j" + 5hat"k"`, then find `2bar("a") + 5bar("b")`
If the vectors `2hat"i" - "q"hat"j" + 3hat"k"` and `4hat"i" - 5hat"j" + 6hat"k"` are collinear then find the value of q
Find `bar("a")*(bar("b") xx bar("c"))`, if `bar("a") = 3hat"i" - hat"j" + 4hat"k", bar("b") = 2hat"i" + 3hat"j" - hat"k", bar("c") = -5hat"i" + 2hat"j" + 3hat"k"`
If `bar("c") = 3bar("a") - 2bar("b")` then prove that `[(bar("a"), bar("b"), bar("c"))]` = 0
The vector having initial and terminal points as (2, 5, 0) and (–3, 7, 4), respectively is ______.
In the triangle `PQR, bar (PQ) = 2bara and bar (QR) = 2barb`. The mid-point of PR is M. Find following vectors in terms of `bar a and bar b`.
- `bar(PR)`
- `bar(PM)`
- `bar(QM)`
What does the vector joining two points represent?
For the vector \[\vec{P_1P_2}\], which point is the initial point?
If \[\overrightarrow{OA}=\vec{a}\] and \[\overrightarrow{OB}=\vec{b}\], what is \[\overrightarrow{AB}\]?
Which expression gives the vector joining \[P_1(x_1,y_1,z_1)\] to \[P_2(x_2,y_2,z_2)\]?
Which statement correctly describes the order of vectors joining two points?
Which expression gives the magnitude of \[\vec{P_1P_2}\] for \[P_1(x_1,y_1,z_1)\] and \[P_2(x_2,y_2,z_2)\]?
What does \[|\vec{P_1P_2}|\] equal?
For \[P(2,3,0)\] and \[Q(-1,-2,-4)\], directed from \[P\] to \[Q\], which point is the terminal point?
What is the magnitude of \[\vec{PQ}=-3\hat{i}-5\hat{j}-4\hat{k}\]?
