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Question: If x + y + z = 0, \| x \| = \| y \| = \| z \| = 2 and q is angle between y and z. then the value of ...

If x + y + z = 0, | x | = | y | = | z | = 2 and q is angle between y and z. then the value of cosec2q + cot2qis equal to

A

4/3

B

5/3

C

1/3

D

1

Answer

5/3

Explanation

Solution

x→+y→+z→=0\overset{\rightarrow}{x} + \overset{\rightarrow}{y} + \overset{\rightarrow}{z} = 0

Ž y→+z→=–x→\overset{\rightarrow}{y} + \overset{\rightarrow}{z} = –\overset{\rightarrow}{x} Ž ∣y→+z→∣2=∣x→∣2|\overset{\rightarrow}{y} + \overset{\rightarrow}{z}|^{2} = |\overset{\rightarrow}{x}|^{2}

Ž∣y→∣2+∣z→∣2+2y→.z→|\overset{\rightarrow}{y}|^{2} + |\overset{\rightarrow}{z}|^{2} + 2\overset{\rightarrow}{y}.\overset{\rightarrow}{z} = ∣x→∣2|\overset{\rightarrow}{x}|^{2}

Ž 4 + 4 + 2 (2) (2) cos q = 4

Ž cos q = –12\frac{–1}{2} Ž q = 1200

Ž cosec2q + cot2q = 43+13=53\frac{4}{3} + \frac{1}{3} = \frac{5}{3}