Question

If none of the vector vector a vector b vector c is 0 hand vector a into vector b is equal to zero and vector b into vector c is equal to zero find the value of vector a into vector

Answer 1

Explanation:

Answer

Let vertor be a

i

^

+b

j

^

+c

k

^

Dot product with

i

^

+

j

^

−3

k

^

=a+b−3c=0 …………(1)

Dot product with

i

^

+3

j

^

−2

k

^

=a+3b−2c=5 ……….(2)

Dot product with 2

i

^

+

j

^

+4

k

^

=2a+b+4c=8 ……………(3)

Equation (2) -Equation (1)

⇒a+3b−2c−a−b+3c=5−0

⇒2b+c=5 ………..(4)

Equation (3)-2× equation (2)

⇒2a+b+4c−2a−6b+4c=8−10

−5b+8c=−2 …………..(5)

Equation (5) - 4× equation (4)

⇒−5b+8c−16b−8c=−2−40

⇒−21b=−42

∴b=

−21

−42

=2

Put b=2 in (4) we get c=5−2b

c=5−2×2=5−4

∴c=1

Put b=2, c=1 in (1)

a+2−3×1=0

a+2−3=0

∴a−1=0

(or) a=1

Hence the verctor is

i

^

+2

j

^

+

k

^

.