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Given A = i + 2j +3k, B = -i + 2j + k and C = 3i + j , find a unit vector in the direction of the resultant of these vectors. Also find a vector D which is normal to both A and B. What is the inclination of
D on C?

Asked by sunil2791 17th November 2017, 7:22 PM
Answered by Expert
Answer:
begin mathsize 16px style Resultant space vector space is space the space sum space of space the space vectors space
3 straight i with hat on top plus 5 straight j with hat on top plus 4 straight k with hat on top
Required space unit space vector space equals fraction numerator 3 straight i with hat on top plus 5 straight j with hat on top plus 4 straight k over denominator square root of 9 plus 25 plus 16 end root end fraction equals fraction numerator 3 straight i with hat on top plus 5 straight j with hat on top plus 4 straight k over denominator 5 square root of 2 end fraction
straight D with rightwards harpoon with barb upwards on top equals straight A with rightwards harpoon with barb upwards on top cross times straight B with rightwards harpoon with barb upwards on top
you space get space minus 4 straight i with hat on top minus 4 straight j with hat on top plus 4 straight k with hat on top
To space find space angle space between space straight D with rightwards harpoon with barb upwards on top space and space straight C with rightwards harpoon with barb upwards on top
Find space it space using space straight D with overparenthesis on top times straight C with rightwards harpoon with barb upwards on top equals open vertical bar straight D with rightwards harpoon with barb upwards on top close vertical bar open vertical bar straight C with rightwards harpoon with barb upwards on top close vertical bar cosθ
you space will space get space straight theta equals cos to the power of negative 1 end exponent open parentheses fraction numerator negative 4 over denominator square root of 30 end fraction close parentheses


end style
Answered by Expert 18th November 2017, 8:01 PM
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