Question

Check whether the following vectors are orthogonal.
A= 2i^+3j^-2k^ ; B= 5i^-2j^+2k^

Answer 1

Answer:

A=2i-3j+5k B=-2i+2j+2k A. B=2×(-2) +(-3) ×2+5 ×2 =-4–6+10 =-10+10 =0 So that A. B=0 ... Find the direction ratios of the given two vectors.

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Answer 2

Answer:

Let unit vector in the plane of 2i+j+k and i−j+k be a=α(2i+j+k)+β(i−j+k)

⇒a=(2α+β)i+(α−β)i+(α+β)k

As a is unit vector, we have

(2α+β)

2

+(α−β)

2

+(α+β)

2

=1

⇒6α

2

+4αβ+3β

2

=1...(i)

As a is orthogonal to 5i+2j+6k we get

5(2α+β)+2(α−β)+6(α+β)=0

⇒18α+9β=0⇒β=−2α

Then from eq (i), we get

6α

2

−8α

2

+12α

2

=1

⇒α=±

10

1

⇒β=∓

10

2

Thus

a=±(

10

3

j−

10

1

k)

Explanation:

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