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Class 10 Class 12

સમતલમાં ગતિ

એક ભૌતિક રાશિને રજૂ કરતો સદિશ $stack straight C space with rightwards arrow on top equals 2 i with overparenthesis on top plus 3 j with overparenthesis on top plus 4 k with overparenthesis on top$ છે, તો X-અક્ષ અને આ સદિશ વચ્ચેનો કોણ .......

$cos to the power of negative 1 end exponent fraction numerator 3 over denominator square root of 29 end fraction$
$cos to the power of negative 1 end exponent fraction numerator 4 over denominator square root of 29 end fraction$
$cos to the power of negative 1 end exponent fraction numerator 5 over denominator square root of 29 end fraction$
$cos to the power of negative 1 end exponent fraction numerator 2 over denominator square root of 29 end fraction$

પ્રક્ષિપ્ત ગતિમાં પદાર્થે પ્રાપ્ત કરેલી મહત્તમ ઊંચાઈ તેની અવધિ કરતાં અડધી હોય, $open parentheses straight H equals 1 half straight R close parentheses$ નો સમક્ષિતિજ સાથેનો પ્રક્ષિપ્ત કોણ $straight theta subscript 0$ .........

$tan to the power of negative 1 end exponent open parentheses 1 close parentheses$
$tan to the power of negative 1 end exponent open parentheses 2 close parentheses$
$tan to the power of negative 1 end exponent open parentheses 3 close parentheses$
$tan to the power of negative 1 end exponent open parentheses 4 close parentheses$

જો $stack straight A space with rightwards arrow on top equals 2 i with overparenthesis on top plus 3 j with overparenthesis on top minus k with overparenthesis on top$ અને $stack straight B space with rightwards arrow on top equals 4 i with overparenthesis on top plus 6 j with overparenthesis on top minus 2 k with overparenthesis on top$ હોય, તો $stack straight A space with rightwards arrow on top$ અને $stack straight B space with rightwards arrow on top$ વચ્ચેનો ખૂણો

$straight pi$
$straight pi over 3$
$straight pi over 2$
$0 to the power of degree$

0 to the power of degree

Tips: -

cos space theta equals fraction numerator A subscript x B subscript x plus A subscript y B subscript y plus A subscript 2 B subscript 2 over denominator square root of A subscript x superscript 2 plus A subscript y superscript 2 plus A subscript z superscript 2 end root square root of B subscript x superscript 2 plus B subscript y superscript 2 plus B subscript z superscript 2 end root end fraction

equals space fraction numerator open parentheses 2 close parentheses open parentheses 4 close parentheses plus open parentheses 3 close parentheses open parentheses 6 close parentheses plus open parentheses negative 1 close parentheses open parentheses negative 2 close parentheses over denominator square root of open parentheses 2 close parentheses squared plus open parentheses 3 close parentheses squared plus open parentheses negative 1 close parentheses squared end root square root of open parentheses 4 close parentheses squared plus open parentheses 6 close parentheses squared plus open parentheses negative 2 close parentheses squared end root end fraction equals fraction numerator 28 over denominator square root of 14 square root of 56 end fraction equals 2 over 2 equals 1 therefore space straight theta equals 0 to the power of degree

એક પદાર્થને $stack straight v space with rightwards arrow on top$ જેટલા વેગથી પ્રક્ષિપ્ત કરવામાં આવે છે. જિ તેની અવધિ મહત્તમ ઊંચાઈ કરતાં બમણી હોય, તો અવધિનું મૂલ્ય .........
(સૂચન : ઉપરના પ્રશ્ન – 6 ના પરિણામનો ઉપયોગ કરો.)

$straight v squared over straight g$
$3 over 5 space v squared over g$
$4 over 5 space v squared over g$
$1 half space v squared over g$

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