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Maths-

General

Easy

Question

If $a with ‾ on top equals 2 i with ‾ on top plus 3 j with ‾ on top plus k with ‾ on top comma a with ‾ on top cross times b with ‾ on top equals 7 i with ‾ on top minus 3 j with ‾ on top minus 5 k with ‾ on top comma a with ‾ on top times b with ‾ on top equals 1$ then $stack b with ‾ on top equals$

$\bar{i} + \bar{j} + 2 \bar{k}$
$\overline{i} + \overline{j} - 2 \overline{k}$
$\overline{i} - \overline{j} + 2 \overline{k}$
$\overline{i} - \overline{j} - 2 \overline{k}$

The correct answer is: $i with ‾ on top minus j with ‾ on top plus 2 k with ‾ on top$

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Chemistry-General

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parallel

If $a with rightwards arrow on top to the power of blank equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i plus j with ˆ on top minus k with ˆ on top$ . Then altitude of the parallel piped formed by the vectors $stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top$ having base formed by $stack b with rightwards arrow on top & stack c with rightwards arrow on top$ is $open parentheses stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top close$ and $a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank$ , $stack c with rightwards arrow on top to the power of ´ end exponent$ are reciprocal system of vectors)

If $a with rightwards arrow on top to the power of blank equals i with ˆ on top plus j with ˆ on top comma b with rightwards arrow on top to the power of ´ equals i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top & c with rightwards arrow on top to the power of ´ equals 2 i plus j with ˆ on top minus k with ˆ on top$ . Then altitude of the parallel piped formed by the vectors $stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top$ having base formed by $stack b with rightwards arrow on top & stack c with rightwards arrow on top$ is $open parentheses stack a with rightwards arrow on top comma stack b with rightwards arrow on top comma stack c with rightwards arrow on top close$ and $a with rightwards arrow on top to the power of blank comma b with rightwards arrow on top to the power of blank$ , $stack c with rightwards arrow on top to the power of ´ end exponent$ are reciprocal system of vectors)

If the four faces of a tetrahedron are represented by the equations $r with minus on top times left parenthesis alpha i with minus on top plus beta j with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis beta j with minus on top plus gamma k with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis gamma k with minus on top plus alpha i with minus on top right parenthesis equals 0$ and $r with minus on top times left parenthesis alpha i with minus on top plus$ $beta j with minus on top plus gamma k with minus on top right parenthesis equals P$ then volume of the tetrahedron (in cubic units) is

If the four faces of a tetrahedron are represented by the equations $r with minus on top times left parenthesis alpha i with minus on top plus beta j with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis beta j with minus on top plus gamma k with minus on top right parenthesis equals 0 comma r with minus on top times left parenthesis gamma k with minus on top plus alpha i with minus on top right parenthesis equals 0$ and $r with minus on top times left parenthesis alpha i with minus on top plus$ $beta j with minus on top plus gamma k with minus on top right parenthesis equals P$ then volume of the tetrahedron (in cubic units) is

If $sum subscript i equals 1 end subscript superscript n end superscript stack a with rightwards arrow on top subscript i end subscript equals stack 0 with rightwards arrow on top$ where $open vertical bar stack a with rightwards arrow on top subscript i end subscript close vertical bar equals 1 for all i$ , then the value of $sum subscript text i end text less or equal than text end text j less or equal than n end subscript stack a subscript i with rightwards arrow on top times a with rightwards arrow on top subscript j$ is

If $sum subscript i equals 1 end subscript superscript n end superscript stack a with rightwards arrow on top subscript i end subscript equals stack 0 with rightwards arrow on top$ where $open vertical bar stack a with rightwards arrow on top subscript i end subscript close vertical bar equals 1 for all i$ , then the value of $sum subscript text i end text less or equal than text end text j less or equal than n end subscript stack a subscript i with rightwards arrow on top times a with rightwards arrow on top subscript j$ is

parallel

The vector $stack O A with minus on top equals negative 2 i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top$ turn by a right angle about origin $left parenthesis 0 right parenthesis$ so that it passes through $j with ˆ on top plus k with ˆ on top$ . then the vector in new position is

The vector $stack O A with minus on top equals negative 2 i with ˆ on top plus j with ˆ on top plus 2 k with ˆ on top$ turn by a right angle about origin $left parenthesis 0 right parenthesis$ so that it passes through $j with ˆ on top plus k with ˆ on top$ . then the vector in new position is

The vectors $a i with ˆ on top plus j with ˆ on top plus k with ˆ on top comma i with ˆ on top plus b j plus k with ˆ on top$ and $i with ˆ on top plus j with ˆ on top plus c k with ˆ on top$ are coplanar where a,b,c are real and distinct from 1 . Then $fraction numerator 1 plus a over denominator 1 minus a end fraction plus fraction numerator 1 plus b over denominator 1 minus b end fraction plus fraction numerator 1 plus c over denominator 1 minus c end fraction equals$

The vectors $a i with ˆ on top plus j with ˆ on top plus k with ˆ on top comma i with ˆ on top plus b j plus k with ˆ on top$ and $i with ˆ on top plus j with ˆ on top plus c k with ˆ on top$ are coplanar where a,b,c are real and distinct from 1 . Then $fraction numerator 1 plus a over denominator 1 minus a end fraction plus fraction numerator 1 plus b over denominator 1 minus b end fraction plus fraction numerator 1 plus c over denominator 1 minus c end fraction equals$

The number of integer values of $p$ for which the vectors $i with ˆ on top plus p squared j with ˆ on top plus p squared k with ˆ on top comma p squared i with ˆ on top plus j with ˆ on top plus p to the power of 4 k with ˆ on top$ and $p to the power of 4 i with ˆ on top plus p to the power of 4 j with ˆ on top plus k with ˆ on top$ are coplanar is

The number of integer values of $p$ for which the vectors $i with ˆ on top plus p squared j with ˆ on top plus p squared k with ˆ on top comma p squared i with ˆ on top plus j with ˆ on top plus p to the power of 4 k with ˆ on top$ and $p to the power of 4 i with ˆ on top plus p to the power of 4 j with ˆ on top plus k with ˆ on top$ are coplanar is

parallel

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