Question

Find the angle between A=i+j+k. and B=-2i-2j-2k


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Answer 1

Answer:

What is the angle between vectors a=I+j+k and b=-i-j+2k?

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A=i+2j-k

b=-i+j-2k

as we know that,for two given vectors a

and b,we have:-

a.b=|a|*|b|*cos a^b

where a^b is the angle between the vectors

a and b

so, a.b= 1*-1+2*1+-1*2=3

|a|=(1+4+1)^1/2=√6

|b|=(1+1+4)^1/2=√6

from the given equation,we have

3=√6*√6*cos a^b

so,cos a^b=3/6=1/2

so angle between the vectors is 60 degree

Answer 2

Answer:

Hey mate here is your answer.....

|a| = √1²+1²+1² = √1+1+1 = √3

|b| = √2²+2²+2² = √12 = 2√3

cos theta = a•b/|a|×|b|

= (i+j+k)•(2i-2j-2k)/|a|×|b|

= (2-2-2)/|a|×|b|

= (-2)/|a|×|b|

= (-2)/√3×2√3

= -1/3

theta = cos^-1(-1/3)

Hope it helps you.....