Discussion Forum : Vector Algebra
Question -
The value of b such that the scalar product of the vector ^i+^j+^k with the unit vector parallel to the sum of the vectors 2^i+4^j+5^k and b^i+2^j+3^k is one, is
Answer: Option D
:
D
The unit vector parallel to the sum of the vectors 2^i+4^j−5^k and b^i+2^j+3^k is
^n=(2+b)^i+6^j−2¨k√(2+b)2+62+(−2)2=(2+b)^i+6^j−2¨k√b2+4b+44
Now,(^i+^j+^k).^n=1
⇒2+b+6−2=√b2+4b+44⇒b=1
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:
D
The unit vector parallel to the sum of the vectors 2^i+4^j−5^k and b^i+2^j+3^k is
^n=(2+b)^i+6^j−2¨k√(2+b)2+62+(−2)2=(2+b)^i+6^j−2¨k√b2+4b+44
Now,(^i+^j+^k).^n=1
⇒2+b+6−2=√b2+4b+44⇒b=1
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