Question

2. Given two vectors A = 3i + 2j + 5k and B = 3i + 3j + hk, determine the
value of h if A and B are perpendicular.​

Answer 1

Answer:

Step-by-step explanation:

We have a=(3  

i

^

−2  

j

^

​  

+  

k

^

) , b=(  

i

^

−3  

j

^

​  

−4  

k

^

) and c=(2  

i

^

+  

j

^

​  

−4  

k

^

)

Since  b+c=a ⇒ (  

i

^

−3  

j

^

​  

−4  

k

^

)  +(2  

i

^

+  

j

^

​  

−4  

k

^

) =(3  

i

^

−2  

j

^

​  

+  

k

^

)

so, a, b and c formed a triangle.

Also,  

a

.  

c

 = (3  

i

^

−2  

j

^

​  

+  

k

^

) .(2  

i

^

+  

j

^

​  

−4  

k

^

)=(+6−2−4)=0

So,  

a

 and  

c

 are perpendicular.

Therefore, a,bandc form  a right angled triangle.

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Answer 2

Answer:

h= -3

Step-by-step explanation:

If two vectors are perpendicular to each other then the dot product will be equal to zero

hence

A . B = cos90°

(3i + 2j + 5k) . (3i + 3j + hk) = 0

9+6+5h = 0

h= -3