Lf P-Q-R-Q-R-P- and R-P-Q- are 3 non-zero vectors- then- a P- - Q- and R- are coplanarb Angle between P- and Q- may be less than 900c P-Q-R- cannot be equal to zerod P-Q- and R- are mutually perpendicular Given P - Q - R - 0

The correct option is B c and d are trueThe three equations tell us that P,Q and nbsp;R are mutually perpendicular to each other. Therefore they are non copl ...

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Standard XII

Physics

Multiplication with Vectors

lf P⃗×Q⃗=R⃗...

Question

lf $\to P \times \to Q = \to R; \to Q \times \to R = \to P$ and $\to R \times \to P = \to Q$ are 3 non-zero vectors, then,
a) $\to P, \to Q$ and $\to R$ are coplanar
b) Angle between $\to P$ and $\to Q$ may be less than $90^{0}$
c) $\to P + \to Q + \to R$ cannot be equal to zero
d) $\to P, \to Q$ and $\to R$ are mutually perpendicular
( Given $P \neq Q \neq R \neq 0$ )

c and d are true

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a, b and c are true

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a and b are true

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d and b are true

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Solution

The correct option is B c and d are true
The three equations tell us that P,Q and R are mutually perpendicular to each other. Therefore they are non coplanar which implies that their sum cannot be equal to zero.
Note: It is assumed that P is not equal to Q which is not equal to R.

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Similar questions

Q. Three vectors

\to P

\to Q

\to R

are such that the

| \to P |

= | \to Q |

| \to R |

= \sqrt{2}

| \to P |

and

\to P + \to Q

+ \to R = 0

. The angle between

\to P

and

\to Q

\to Q

and

\to R

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\to P

and

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Q. If

[\to p + 2 \to q + 3 \to r \to q + 2 \to r + 3 \to p \to r + 2 \to p + 3 \to q] = 54

where

\to p

\to q

and

\to r

are three vector then the Value of

∣ ∣ ∣ ∣ \begin{matrix} \to p . \to p & \to p . \to q & \to p . \to r \to p . \to q & \to q . \to q & \to q . \to r \to p . \to r & \to r . \to q & \to r . \to r \end{matrix} ∣ ∣ ∣ ∣

Q. Let

\to p, \to q, \to r

be three mutually perpendicular vectors of the same magnitude. lf a vector

\to x

satisfies the equation

\to p \times {(\to x - \to q) \times \to p} + \to q \times {(\to x - \to r) \times \to q} + \to r \times {(\to x - \to p) \times \to r}

is given by

Q. Let

\to p, \to q, \to r

be three mutually perpendicular vectors of the same magnitude If a vector

\to x

satisfies the equation

\to p \times ((\to x - \to q) \times \to p) + \to q \times ((\to x - \to r) \times \to q) + \to r \times ((\to x - \to p) \times \to r) = 0

is given by

Q. If

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lf →P×→Q=→R;→Q×→R=→P and →R×→P=→Q are 3 non-zero vectors, then, a) →P,→Q and →R are coplanarb) Angle between →P and →Q may be less than 900c) →P+→Q+→R cannot be equal to zerod) →P,→Q and →R are mutually perpendicular( Given P≠Q≠R≠0 )

The correct option is B c and d are trueThe three equations tell us that P,Q and R are mutually perpendicular to each other. Therefore they are non coplanar which implies that their sum cannot be equal to zero.Note: It is assumed that P is not equal to Q which is not equal to R.

The correct option is B c and d are true
The three equations tell us that P,Q and R are mutually perpendicular to each other. Therefore they are non coplanar which implies that their sum cannot be equal to zero.
Note: It is assumed that P is not equal to Q which is not equal to R.