Three vectors P- -Q- R- are shown in figure let S be any point on the vector R- the dirt- Between P S is if - R- find the general equation between P-Q S-

S⃗ = P⃗ + b |R⃗ | #160; R̂ #160; #160;= P⃗ + b | R⃗ | R⃗| R⃗ | #160; #160;= P⃗ + b R⃗ #160; #160;= P⃗ + b ( Q⃗ P⃗ ) ...

You visited us 1 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Mathematics

Dot Product

Three vectors...

Question

Three vectors $\to P, \to Q$ & $\to R$ are shown in figure let $S$ be any point on the vector $\to R$ , the dirt. Between $P$ & $S$ is if $∣ ∣ \to R ∣ ∣$ find the general equation between $P, Q$ & $S$ .

Open in App

Solution

$\to S = \to P + b | \to R |^R$

= $\to P + b | \to R | \frac{\to R}{| \to R |}$

= $\to P + b \to R$

= $\to P + b (\to Q - \to P)$

= $(1 - b) \to P + b \to Q$

Suggest Corrections

Similar questions

Q. Three vectors

\to P

\to Q

and

\to R

are shown in figure. Let

S

be any point on the vector

\to R

. The distance between the points

P

and

S

b ∣ \to R ∣

. The general relation among vectors

\to P

\to Q

and

\to S

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. 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

and

\to P

and

\to R

will be respectively.

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 [(\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] = \to 0

, then

\to x

is given by

Join BYJU'S Learning Program

Three vectors →P,→Q & →R are shown in figure let S be any point on the vector →R, the dirt. Between P & S is if ∣∣→R∣∣ find the general equation between P,Q & S.

→S=→P+b|→R|^R = →P+b|→R|→R|→R| = →P+b→R = →P+b(→Q−→P) = (1−b)→P+b→Q

Three vectors $\to P, \to Q$ & $\to R$ are shown in figure let $S$ be any point on the vector $\to R$ , the dirt. Between $P$ & $S$ is if $∣ ∣ \to R ∣ ∣$ find the general equation between $P, Q$ & $S$ .

$\to S = \to P + b | \to R |^R$

= $\to P + b | \to R | \frac{\to R}{| \to R |}$

= $\to P + b \to R$

= $\to P + b (\to Q - \to P)$

= $(1 - b) \to P + b \to Q$