The direction cosines of vector $( A - B )$, if $A =2 \hat{ i }+3 \hat{ j }+\hat{ k }, B =2 \hat{ i }+2 \hat{ j }+3 \hat{ k }$ are
- A$0, \frac{1}{\sqrt{5}}, \frac{-2}{\sqrt{5}}$
- B$0, \frac{2}{\sqrt{5}}, \frac{1}{\sqrt{5}}$
- C$0,0, \frac{1}{\sqrt{5}}$
- DNone of the above
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The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j - 2\hat k} \right)$ and $\vec B = \left( {5\hat i - 6\hat j - y\hat k} \right)$ may be parallel are
The values of $x$ and $y$ for which vectors $\vec A = \left( {6\hat i + x\hat j - 2\hat k} \right)$ and $\vec B = \left( {5\hat i - 6\hat j - y\hat k} \right)$ may be parallel are
There are four forces acting at a point $P$ produced by strings as shown in figure, point $P$ is at rest. The forces $F_1$ and $F_2$ are respectively:-
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Find the magnitude of the unknown forces $X$ and $Y$ if sum of all forces is zero
Find the magnitude of the unknown forces $X$ and $Y$ if sum of all forces is zero
Two vectors of magnitude $3$ & $4$ have resultant which make angle $\alpha$ & $\beta$ respectively with them $\{given\, \alpha + \beta \neq 90^o\}$
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For component of a vector $A =(3 \hat{ i }+4 \hat{ j }-5 \hat{ k })$, match the following colum.
Colum $I$
Colum $II$
$(A)$ $x-$axis
$(p)$ $5\,unit$
$(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$
$(q)$ $4\,unit$
$(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$
$(r)$ $0$
$(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$
$(s)$ None
| Colum $I$ | Colum $II$ |
| $(A)$ $x-$axis | $(p)$ $5\,unit$ |
| $(B)$ Along another vector $(2 \hat{ i }+\hat{ j }+2 \hat{ k })$ | $(q)$ $4\,unit$ |
| $(C)$ Along $(6 \hat{ i }+8 \hat{ j }-10 \hat{ k })$ | $(r)$ $0$ |
| $(D)$ Along another vector $(-3 \hat{ i }-4 \hat{ j }+5 \hat{ k })$ | $(s)$ None |