Question

Main Menu ContentsGrades Course Contents »... » bioSet01 » Vector operations Vector operations Points:1 The labelled vectors below are drawn to scale. For each of the statements select Greater than, Less than, or Equal to. Less than B H . N is o Greater than S U is... 0 Equal to 1 Y x ונ is 0. Less than U . Y is O. Greater than IR x J is 0 Less thanThe magnitude of R... that of S

Answer 1

Remember that for dot product

a.b = |a|*|b|*cos $\theta$

for cross product

|axb| = |a|*|b|*sin $\theta$

Now Using these properties:

(i)

H.N = |H|*|N|*cos $\theta$

$\theta$ = Angle between H and N

from the figure we can see that

$\theta$ = 135 deg

cos 135 deg = -0.707

Since |H| and |N| are positive, So

H.N = (+ve)*(+ve)*(-ve) = -ve

H.N is less than 0

(ii)

S.U = |S|*|U|*cos $\theta$

$\theta$ = Angle between H and N

from the figure we can see that

$\theta$ = 90 deg

cos 90 deg = 0

S.U = (+ve)*(+ve)*(0) = 0

S.U is equal to 0

(iii)

|YXJ| = |Y|*|J|*sin $\theta$

$\theta$ = Angle between Y and J

from the figure we can see that

$\theta$ = 0 deg

sin 90 deg = 0

|YXJ| = (+ve)*(+ve)*(0) = 0

|YXJ| is equal to 0

(iv)

U.Y = |U|*|Y|*cos $\theta$

$\theta$ = Angle between U and Y

from the figure we can see that

$\theta$ = 180 deg

cos 180 deg = -1

U.Y = (+ve)*(+ve)*(-ve) = -ve

U.Y is less than 0

(v)

|RXJ| = |R|*|J|*sin $\theta$

$\theta$ = Angle between R and J

from the figure we can see that

$\theta$ = 45 deg

sin 45 deg = 0.707

|RXJ| = (+ve)*(+ve)*(+ve) = +ve

|RXJ| is greater than 0

(vi)

Since we know that in a square

length of diagonal is greater than length of side of square, So here in the figure S is diagonal of square of 2x2 and R is side of square of 2x2. So

The magnitude of R less than that of S

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