The position vectors of points A - B - C and D are A -3 -4 -5 k- B -4 -5 -6 k- C -7 -9 -3 k- and D -4 -6 - - Then- thedisplacement vectors AB and CD areA- parallelB- antiparallelC- perpendicularD- inclined at an angle of 60-

The correct option is B antiparallelWe know, AB=B A AB=(4î+5ĵ+6k̂) (3î+4ĵ+5k̂) AB=î+ĵ+k̂ Similarly, CD=D C CD=(4î+6ĵ) (7î+9ĵ+3k̂) CD= 3î 3ĵ 3k̂ So we can writ ...

You visited us 4 times! Enjoying our articles? Unlock Full Access!

Byju's Answer

Standard XII

Physics

Vector Addition

The position ...

Question

The position vectors of points $A, B, C$ and $D$ are $A = 3^i + 4^j + 5^k, B = 4^i + 5^j + 6^k$ , $C = 7^i + 9^j + 3^k$ and $D = 4^i + 6^j$ . Then, the displacement vectors $A B$ and $C D$ are

perpendicular

No worries! We‘ve got your back. Try BYJU‘S free classes today!

parallel

No worries! We‘ve got your back. Try BYJU‘S free classes today!

antiparallel

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

inclined at an angle of

60^{\circ}

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

Solution

The correct option is C antiparallel
We know,
$- - \to A B = \to B - \to A$
$- - \to A B = (4^i + 5^j + 6^k) - (3^i + 4^j + 5^k)$
$- - \to A B =^i +^j +^k$
Similarly,
$- - \to C D = \to D - \to C$
$- - \to C D = (4^i + 6^j) - (7^i + 9^j + 3^k)$
$- - \to C D = - 3^i - 3^j - 3^k$

So we can write, $- - \to C D = - 3 (- - \to A B)$ .
$∴$ Vectors AB and CD are antiparallel

Suggest Corrections

Similar questions

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k

B = 4^i + 5^j + 6^k, C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

, then the displacement vectors

- - \to A B

and

- - \to C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k

B = 4^i + 5^j + 6^k, C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

, then the displacement vectors

- - \to A B

and

- - \to C D

are

Q. The position vectors of points

A, B, C

and

D

are

A = 3^i + 4^j + 5^k, B = 4^i + 5^j + 6^k

C = 7^i + 9^j + 3^k

and

D = 4^i + 6^j

. Then, the displacement vectors

A B

and

C D

are

Q. If the position vectors

\to A, \to B, \to C, and \to D

are

\to A = 3^i + 4^j + 5^k, \to B = 4^i + 5^j + 6^k, \to C = 7^i + 9^j + 3^k,

and

\to D = 4^i + 6^j,

then the displacement vectors

- - \to A B and - - \to C D

are

Q. If the position vectors of

A, B, C, D

are

3^i + 2^j +^k, 4^i + 5^j + 5^k, 4^i + 2^j - 2^k, 6^i + 5^j -^k

respectively then the position vector of the point of intersection of

¯ A B

and

¯ C D

Join BYJU'S Learning Program

The position vectors of points A,B,C and D are A=3^i+4^j+5^k, B=4^i+5^j+6^k, C=7^i+9^j+3^k and D=4^i+6^j. Then, the displacement vectors AB and CD are

The position vectors of points $A, B, C$ and $D$ are $A = 3^i + 4^j + 5^k, B = 4^i + 5^j + 6^k$ , $C = 7^i + 9^j + 3^k$ and $D = 4^i + 6^j$ . Then, the displacement vectors $A B$ and $C D$ are