Tip:A–D to answerE for explanationV for videoS to reveal answer
Number of vectors of unit length perpendicular to the vectors a=2i^+j^+2k^ and b=j^+k^ is
- A.
one
- B.
two
(Correct Answer) - C.
three
- D.
infinite
Explanation
1. Find the cross product (a×b):
n=i^20amp;j^amp;1amp;1amp;k^amp;2amp;1
n=i^(1−2)−j^(2−0)+k^(2−0)
2. Magnitude of n:
∣n∣=(−1)2+(−2)2+22=1+4+4=3
3. Unit vectors perpendicular to both a and b:
Final Answer:
The number of vectors is:
Explanation
1. Find the cross product (a×b):
n=i^20amp;j^amp;1amp;1amp;k^amp;2amp;1
n=i^(1−2)−j^(2−0)+k^(2−0)
2. Magnitude of n:
∣n∣=(−1)2+(−2)2+22=1+4+4=3
3. Unit vectors perpendicular to both a and b:
Final Answer:
The number of vectors is:
