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Vector CalculusQuestion and Answers: Page 4

Question Number 100320 Answers: 1 Comments: 0

Evaluate ∫∫_s F^→ .n^ dS where F^→ =4xi^ −2y^2 j^ +z^2 k^ and S is the surface of the cylinder bounded by x^2 +y^2 =4 ,z = 0 and z=3 .

$Evaluate \int \int_{s} \vec{F} . \hat{n} dS where \vec{F} = 4 x \hat{i} - {2 y}^{2} \hat{j} + z^{2} \hat{k}$ $and S is the surface of the cylinder$ $bounded by x^{2} + y^{2} = 4, z = 0 and z = 3 .$

Question Number 100074 Answers: 1 Comments: 0

Question Number 98119 Answers: 0 Comments: 1

Find the shortest distance between the skew lines ((x−3)/3) = ((8−y)/1) = ((z−3)/1) and ((x+3)/(−3)) = ((y+7)/2) = ((z−6)/4) .

$Find the shortest distance between the$ $skew lines \frac{x - 3}{3} = \frac{8 - y}{1} = \frac{z - 3}{1} and$ $\frac{x + 3}{- 3} = \frac{y + 7}{2} = \frac{z - 6}{4} .$

Question Number 97901 Answers: 2 Comments: 2

Question Number 97353 Answers: 5 Comments: 0

Question Number 95509 Answers: 2 Comments: 0

find the angle of plane 2x−y+2z=1 and x+3y−2z = 2

$find the angle of plane$ $2 x - y + 2 z = 1 and x + 3 y - 2 z = 2$

Question Number 92143 Answers: 0 Comments: 1

fond∫((2x)/(1+x^2 ))dx

$f o n d \int \frac{2 x}{1 + x^{2}} d x$

Question Number 92138 Answers: 2 Comments: 0

∫(dx/(1+x^2 ))

$\int \frac{d x}{1 + x^{2}}$

Question Number 84969 Answers: 0 Comments: 0

let c is a constant vector and r^→ =xi^ +yj^ +zk^ then proved that grad ∣c×r^→ ∣^n =n∣c×r^→ ∣^(n−2) c×(r^→ ×c).

$let c is a constant vector and \vec{r} = x \hat{i} + y \hat{j} + z \hat{k} then proved that grad ∣ c \times \vec{r} ∣^{n} = n ∣ c \times \vec{r} ∣^{n - 2} c \times (\vec{r} \times c) .$

Question Number 84624 Answers: 1 Comments: 0

find grad r^m where r=x^2 +y^2 +z^2

$find grad r^{m} where r = x^{2} + y^{2} + z^{2}$

Question Number 80402 Answers: 0 Comments: 0

Question Number 78522 Answers: 0 Comments: 10

what is the line passing through (2,2,1) and parallel to 2i^ − j^ − k^ ?

$w h a t i s t h e$ $l i n e p a s s i n g t h r o u g h (2, 2, 1)$ $a n d p a r a l l e l t o 2 \hat{i} - \hat{j} - \hat{k} ?$

Question Number 76302 Answers: 1 Comments: 0

given vektor a=(3,x,−2) b=(−6,−2,y) . what the value x and y if a and b are parallel?

$g i v e n v e k t o r a = (3, x, - 2)$ $b = (- 6, - 2, y) . w h a t t h e v a l u e x$ $a n d y i f a a n d b a r e p a r a l l e l ?$

Question Number 75101 Answers: 4 Comments: 2

the vector equations of two lines L_1 and L_2 is given by L_1 :r= i−j+3k + λ(i−j +k) L_2 : r= 2i+aj + 6k + μ(2i + j + 3k) where a,λ,μ are real constants. given that L_1 and L_2 intersect find a. the value of the constant a. b. the position vector of the point of intersection between L_1 and L_2 c. the cosine of the acute angle between L_1 and L_2 please help

$t h e v e c t o r e q u a t i o n s o f t w o l i n e s L_{1} a n d L_{2} i s g i v e n b y$ $L_{1} : r = i - j + 3 k + λ (i - j + k)$ $L_{2} : r = 2 i + a j + 6 k + μ (2 i + j + 3 k)$ $w h e r e a, λ, μ a r e r e a l c o n s t a n t s .$ $g i v e n t h a t L_{1} a n d L_{2} i n t e r s e c t f i n d$ $a . t h e v a l u e o f t h e c o n s t a n t a .$ $b . t h e p o s i t i o n v e c t o r o f t h e p o i n t o f$ $i n t e r s e c t i o n b e t w e e n L_{1} a n d L_{2}$ $c . t h e c o s i n e o f t h e a c u t e a n g l e b e t w e e n L_{1} a n d L_{2}$ $p l e a s e h e l p$

Question Number 71198 Answers: 0 Comments: 0

A particle P is projected from a point O at the edge of a cliff 60m from the sea with a velocity of 30ms^(−1) . When P is at a point B where OB is a horizontal, another particle Qsuch that P and Q hit the sea simultaneously at thesame point A. Gven that they strike the sea 6seconds after P was fired ^ calculate a) the sine of the angle of elevation of projection. b) the distance from A to O. c) the time of flight of Q. d) the Range . (take g = 10ms^(−2) ) please help

$A p a r t i c l e P i s p r o j e c t e d f r o m a p o i n t O a t t h e e d g e o f a c l i f f 60 m$ $f r o m t h e s e a w i t h a v e l o c i t y o f 30 {m s}^{- 1} . W h e n P i s a t a p o i n t B$ $w h e r e O B i s a h o r i z o n t a l, a n o t h e r p a r t i c l e Q s u c h t h a t$ $P a n d Q h i t t h e s e a s i m u l t a n e o u s l y a t t h e s a m e p o i n t A . G v e n t h a t t h e y$ $s t r i k e t h e s e a 6 s e c o n d s a f t e r P w a s f i r e d \bar{} c a l c u l a t e$ $a) t h e s i n e o f t h e a n g l e o f e l e v a t i o n o f p r o j e c t i o n .$ $b) t h e d i s t a n c e f r o m A t o O .$ $c) t h e t i m e o f f l i g h t o f Q .$ $d) t h e R a n g e .$ $(t a k e g = 10 {m s}^{- 2})$ $p l e a s e h e l p$

Question Number 70876 Answers: 0 Comments: 0

Prove that The necessary and sufficient condition that the curve be plane (curve) is [r′,r′′,r′′′]=0. OR A curve is plane curve iff τ=0.

$Prove that$ $The necessary and sufficient condition$ $that the curve be plane (curve) is$ $[r^{'}, r^{″}, r^{‴}] = 0 .$ $OR$ $A curve is plane curve iff τ = 0 .$

Question Number 68836 Answers: 1 Comments: 0

Show that the graph of r = (sin t)i + (2cos t)j + ((√3)sin t)k is a circle

$Show that the graph of$ $r = (\sin t) i + (2 \cos t) j + (\sqrt{3} \sin t) k$ $is a circle$

Question Number 65797 Answers: 1 Comments: 0

find the constant a,b and c so that the direction derivative of Φ=axy^2 +byz+cz^2 x^3 at (1,2,−1) has a maximum of magnitude 64 jn a direction parallel to the z axis.

$f i n d t h e c o n s t a n t a, b a n d c s o$ $t h a t t h e d i r e c t i o n d e r i v a t i v e o f$ $Φ = {a x y}^{2} + b y z + {c z}^{2} x^{3} a t (1, 2, - 1)$ $h a s a m a x i m u m o f m a g n i t u d e$ $64 j n a d i r e c t i o n p a r a l l e l t o t h e$ $z a x i s .$

Question Number 65261 Answers: 0 Comments: 1

solve4−xy+yz−xz

$s o l v e 4 - x y + y z - x z$

Question Number 64456 Answers: 0 Comments: 1

Question Number 64011 Answers: 1 Comments: 3

lim_(x→0) ((x^x −1)/(xlnx))

$li \underset{x \to 0}{m} \frac{x^{x} - 1}{xlnx}$

Question Number 62517 Answers: 4 Comments: 2

Question Number 61258 Answers: 1 Comments: 2

Calculate, using cartesian coodinates, the following integrals: 1) ∫∫_D dxdy being D={ (x,y)∈R^2 /0≤x≤(1/2),y+x≤1,y≥0} 2) ∫∫_D x^3 ydxdy being D={(x,y)∈R^2 /0≤x≤(1/2),y+x≤1,y≥0} 3) ∫∫_D (x/y)dxdy being D={(x,y)∈R^2 /xy≤16,x≥y,x−6≤y,x≥0,y≥1} Help please!

$C a l c u l a t e, u s i n g c a r t e s i a n c o o d i n a t e s, t h e f o l l o w i n g$ $i n t e g r a l s :$ $1) \int \int_{D} d x d y b e i n g D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ \frac{1}{2}, y + x ⩽ 1, y ⩾ 0}$ $2) \int \int_{D} x^{3} y d x d y b e i n g D = {(x, y) \in R^{2} / 0 ⩽ x ⩽ \frac{1}{2}, y + x ⩽ 1, y ⩾ 0}$ $3) \int \int_{D} \frac{x}{y} d x d y b e i n g D = {(x, y) \in R^{2} / x y ⩽ 16, x ⩾ y, x - 6 ⩽ y, x ⩾ 0, y ⩾ 1}$ $H e l p p l e a s e!$

Question Number 60015 Answers: 0 Comments: 0

Question Number 60013 Answers: 0 Comments: 0

Question Number 59932 Answers: 0 Comments: 0

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