Three points whose position vectors are a + b, , ,a - b and a + k… - Vidyadip

MCQ

Three points whose position vectors are $a + b,\,\,a - b$ and $a + kb$ will be collinear, if the value of $k $ is

A
Zero
B
Only negative real number
C
Only positive real number
✓
Every real number

✓

Answer

Correct option: D.

Every real number

d
(d) $\overrightarrow {AB} = \lambda \overrightarrow {BC} $, (for collinearity)

Here $\overrightarrow {AB} = - 2b,$ $\overrightarrow {BC} = (k + 1)b$

Hence $\forall \,\,k \in R \Rightarrow \overrightarrow {AB} = \lambda \overrightarrow {BC} .$

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from 10. vector algebra→10. vector algebra — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $a, b$ be two fixed positive integers such that $f(a + x) = b + {[{b^3} + 1 - 3{b^2}f(x) + 3b{\{ f(x)\} ^2} - {\{ f(x)\} ^3}]^{\frac{1}{3}}}$ for all real $x$, then $f(x)$ is a periodic function with period

$\int {\frac{{{e^{{{\tan }^{ - 1}}\sqrt x }}}}{{\sqrt x + x\sqrt x }}dx = } $

If $\left[ {a \times b\;\;b \times c\;\;c \times a} \right] = \alpha \;{\left[ {a\;\;b\;\;c} \right]^2}$ then $\lambda$ is equal to

If $\hat x,\,\hat y$ and $\hat z$ are three unit vectors in three dimensional space , then the minimum value of ${\left| {\hat x + \hat y} \right|^2}\, + \,{\left| {\hat y + \hat z} \right|^2}\, + \,{\left| {\hat z + \hat x} \right|^2}$

The differential equation of the family of curves represented by the equation ${x^2}y = a$, is

The value of the integral $\int\limits^2_{-2}\big|1-\text{x}^2\big|\text{dx}$ is:

4
2
-2
0

If $\text{f}(\text{x})=\text{e}^{\text{x}}\sin\text{x}$ in $[0,\pi],$ then c in Rolle's theorem is:

$\frac{\pi}{6}$
$\frac{\pi}{4}$
$\frac{\pi}{2}$
$\frac{3\pi}{4}$

Choose the correct answer out of the given four options.

Let * be binary operation defined on R by a * b = 1 + ab ∀ a, b ∈ R. Then the operation * is:

Commutative but not associative.
Associative but not commutative.
Neither commutative nor associative.
Both commutative and associative.

If $\theta$ is an acute angle and the vector $(\sin\theta)\hat{\text{i}}+(\cos\theta)\hat{\text{j}}$ is perpendicular to the vector $\hat{\text{i}}-\sqrt{3}\hat{\text{j}},$

$\frac{\pi}{6}$
$\frac{\pi}{5}$
$\frac{\pi}{4}$
$\frac{\pi}{3}$

The straight lines $\frac{{x - 1}}{1} = \frac{{y - 2}}{2} = \frac{{z - 3}}{3}$ and $\frac{{x - 1}}{2} = \frac{{y - 2}}{2} = \frac{{z - 3}}{{ - 2}}$ are