Consider the set of eight vectors V - ai - bj - ck a- b- c - -1- 1- Three non-coplanar vectors can be chosen from V in 2 p ways- then p is

The correct option is B 5 Let (1, 1, 1), ( 1, 1, 1), (1, 1, 1), ( 1, 1, 1) be vectors a⃗, #160;b⃗, #160;c⃗, #160;d⃗ , rest of the vecto ...

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Standard XII

Physics

Displacement in 2D Motion

Consider the ...

Question

Consider the set of eight vectors $V = {a ˆ i + b ˆ j + c ˆ k$ $a, b, c \in {- 1, 1}}$ . Three non-coplanar vectors can be chosen from $V$ in 2 $^{p}$ ways, then p is

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Solution

The correct option is B $5$
Let $(1, 1, 1), (- 1, 1, 1), (1, - 1, 1), (- 1, - 1, 1)$ be vectors $\to a, \to b, \to c, \to d$ , rest of the vectors are $- \to a, - \to b, - \to c, - \to d$ and let us find the number of ways of selecting co-planar vectors.

Observe that out of any three coplanar vectors two will be collinear (anti parallel).
Number of ways of selecting the anti-parallel pair $= 4$
Number of ways of selecting the third vector $= 6$
Total $= 24$
Number of non-coplanar selections
$=^{8} C_{3} - 24 = 32 = 2^{5}, p = 5$
$∴ p = 5$

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Consider the set of eight vectors V={aˆi+bˆj+cˆk a,b,c∈{−1,1}}. Three non-coplanar vectors can be chosen from V in 2p ways, then p is

Consider the set of eight vectors $V = {a ˆ i + b ˆ j + c ˆ k$ $a, b, c \in {- 1, 1}}$ . Three non-coplanar vectors can be chosen from $V$ in 2 $^{p}$ ways, then p is