Question

Please find all Unit Vectors lying on the Line : x = 2y = -z​

Answer 1

Answer:

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Step-by-step explanation:

Vector perpendicular to both lines = cross product of their direction ratios

=

∣

∣

∣

∣

∣

∣

∣

∣

i

^

3

1

j

^

1

2

k

^

2

3

∣

∣

∣

∣

∣

∣

∣

∣

=

i

^

(3−4)−

j

^

(9−2)+

b

^

(6−1)

=−

i

^

−7

j

^

+5

k

^

unit vector =

(1)

2

−(7)

2

+(5)

5

−

i

^

−7

j

^

+5

k

^

=

5

3

−

i

^

−7

j

^

+5

k

^

S

Answer 2

Step-by-step explanation:

x = 2y = - z gives

x/2 = y = z/ -2

Hence , vectors lying on the line are

2 I + j - 2k and -2 I - j + 2k

unit vectors lying on the line are

1/3 (I2 i+ j - 2k ) and 1/3 (-2 I - j + 2k).