The two vectors $\vec A = -2\widehat i + \widehat j + 3\widehat k$ and $\vec B = 7\widehat i + 5\widehat j + 3\widehat k$ are :-
- AParallel
- BPerpendicular
- CAntiparallel
- DNone of the above
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The area of the parallelogram having diagonals ${3\hat i}\,\, + \,\,\hat j\,\, - \,\,2\hat k$ and $\hat i\,\, - \,\,3\hat j\,\, + \;\,4\hat k$ is
The area of the parallelogram having diagonals ${3\hat i}\,\, + \,\,\hat j\,\, - \,\,2\hat k$ and $\hat i\,\, - \,\,3\hat j\,\, + \;\,4\hat k$ is
If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$. Then the value of $\alpha $ is
If a vector $2\hat i + 3\hat j + 8\hat k$ is perpendicular to the vector $4\hat j - 4\hat i + \alpha \hat k$. Then the value of $\alpha $ is
- [AIPMT 2005]
The values of $x$ and $y$ for which vectors $A =(6 \hat{ i }+x \hat{ j }-2 \hat{ k })$ and $B =(5 \hat{ i }+6 \hat{ j }-y \hat{ k })$ may be parallel are
The position vectors of points $A, B, C$ and $D$ are $A = 3\hat i + 4\hat j + 5\hat k,\,\,B = 4\hat i + 5\hat j + 6\hat k,\,\,C = 7\hat i + 9\hat j + 3\hat k$ and $D = 4\hat i + 6\hat j$ then the displacement vectors $AB$ and $CD $ are
The position vectors of points $A, B, C$ and $D$ are $A = 3\hat i + 4\hat j + 5\hat k,\,\,B = 4\hat i + 5\hat j + 6\hat k,\,\,C = 7\hat i + 9\hat j + 3\hat k$ and $D = 4\hat i + 6\hat j$ then the displacement vectors $AB$ and $CD $ are
Vector $A$ is pointing eastwards and vector $B$ northwards. Then, match the following two columns.
Colum $I$
Colum $II$
$(A)$ $(A+B)$
$(p)$ North-east
$(B)$ $(A-B)$
$(q)$ Vertically upwards
$(C)$ $(A \times B)$
$(r)$ Vertically downwards
$(D)$ $(A \times B) \times(A \times B)$
$(s)$ None
| Colum $I$ | Colum $II$ |
| $(A)$ $(A+B)$ | $(p)$ North-east |
| $(B)$ $(A-B)$ | $(q)$ Vertically upwards |
| $(C)$ $(A \times B)$ | $(r)$ Vertically downwards |
| $(D)$ $(A \times B) \times(A \times B)$ | $(s)$ None |