The position vectors of points A- B- C and D are A-3-4-5k- B-4-5-6k- C-7-9-3k- and D-4-6- Then- the displacement vectors AB and CD are

We 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 write, CD= 3(AB). ∴ Vectors AB and CD are ...

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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

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parallel

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antiparallel

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inclined at an angle of

60^{\circ}

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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

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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