Vectors A⃗ and B⃗ lie in an x y plane. A⃗ has magnitude 8.00...

Vectors $\vec{A}$ and $\vec{B}$ lie in an $x y$ plane. $\vec{A}$ has magnitude 8.00 and angle $130^{\circ} ; \vec{B}$ has components $B_{x}=-7.72$ and $B_{y}=-9.20$ . (a) What is 5$\vec{A} \cdot \vec{B}$ ? What is 4$\vec{A} \times 3 \vec{B}$ in $(\mathrm{b})$ unit-vector notation and (c) magnitude-angle notation with spherical coordinates Fig. $3-34$ ? (d) What is the angle between the directions of $\vec{A}$ and 4$\vec{A} \times 3 \vec{B} ?($Hint: Think a bit before you resort to a calculation.) What is $\vec{A}+3.00 \hat{\mathrm{k}}$ in (e) unit-vector notation and (f) magnitude- angle notation with spherical coordinates?

Transcript

00:01 Of vector a is 8 and the angle is given which is 130 degree so from here we can write as vector a is equals to 8 .00 cos 130 degree plus 8 .00 sign 130 j i so after putting the all this value we get the value of vector a at minus 5 .14 i plus 6 .128 j and similarly we are given vector b and for this we get the value of vector we at 7 .721 i minus 9 .20 j so from here we can find out in the part when we have to find out the 5a b so from here what we do we just put the value of a and b which we just calculative which is 5 multiplied by minus 5 .14i plus 6 .128 j multiply by minus 7 .7212 to i minus 9 .20j.

01:16 So after solving all this value we get the value of 5abs minus 83 .488.

01:23 So this is the answer to the part a.

01:29 So in the part b we have to find out the value of 480.

01:34 Multiply by 3b so again we just have to put the values of a and b which is minus 5 .14 i plus 6 .128 j multiply by 3 multiplied by minus 7 .72 i minus 9 .20 j after solving this values we get the value 4a multiplied by 3 b as 567 .456k plus 5 666 7 .42k.

02:06 So after solving this value we get the value of 4a minus multiply by 3 v as 1134 multiply 876k so this is the answer to the part b now in the second part we have to find out the value of 4a cross 3b so here in this value of 3a cross 3b so here in the value of is x square plus y square plus red squares the whole power to one by two so from here the value of x is zero the value of y is zero and the value of z is 134 .876 and it's all squares whole root so from here we get the value of 4a cross 3b as uh one -one three four point eight seventy six uh and from here theta is equals to r10 y divided by x and the value of y is zero and the value of x is also zero so this is not defined now in the another the value of pi is given as arc pi is equals to arc gz by r and the value of z z is z is z is 1134 .876 and the value for r is 1134 .876.

03:37 From here we can say that the value of pi is 0.

03:41 So from here we can write it as 4a cross 3b is equals to 1134 .876...

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